Patent Publication Number: US-2007106593-A1

Title: Adaptive stochastic transaction system

Description:
BACKGROUND  
      1. Field of the Invention  
      The present invention generally relates to transaction systems and particularly to commercial transaction systems, for example, business-to-consumer transaction systems.  
      2. Background Art  
      Commercial transactions and transaction systems can be traced back into human prehistory. In a simple archetypal transaction, two parties exchange or agree to exchange respective objects. In general, the desirability of an object to a given party may be determined by both objective factors (e.g., scarcity) and subjective factors (e.g., symbolism), which factors may be independent, correlated, or a combination thereof. Taken together, the factors correspond to the value ascribed to a particular object. Although objective factors may be determinable to both parties, subjective factors often may be less so. Thus, an object may be valued differently by the respective parties intending to exchange objects. Typically, parties intending to effect an exchange undertake some form of interaction, by which the prospective traders reach a meeting of the minds on the terms of trade. These interactions are an essential prerequisite to nearly every type of transaction. For a given exchange, a series of such interactions may be called a negotiation. Over time, structured protocols, including formal negotiations, have evolved to facilitate certain transactions. Many everyday transactions, however, rely on informal negotiations for the trading parties to reach an accord.  
      To facilitate trading between parties drawn from a diverse range of social and political groups living in disparate geographic locations, the use of a common substitute object as an intermediate medium of exchange was long ago devised as a necessary convenience. Fundamental to this common intermediate construct is the principle that the common substitute object was ascribed a value which as generally agreed upon by all transacting parties. In one form, the common substitute is called money. Money allows two parties to effect a transaction, in which one party (here, the buyer) provides money to the other party (here, the seller), in exchange for the desired object. The seller may then exchange received money for objects desired by the seller. In the former transaction, a seller represents the value of an exchange object with a characteristic called a price.  
      Another fundamental principle of transactions is the notion of fairness. Usually, the seller intends to sell an object at the highest attainable price, with the difference in value between his cost and the selling price representing his profit. Parties typically understand that the seller may obtain some profit from a transaction, and that the price the buyer is willing to pay represents the most that a buyer wishes to pay for the particular object. Customarily, the fairness of a transaction can be profoundly and negatively affected by deception or manipulation of the price or quantity of an object by a buyer, a seller, or a third party. At the same time, a transaction is considered to be fair if the objects to be exchanged have comparable value to the transactors. If a transaction, or deal, is considered to be fair, both buyer and seller are likely to execute the transaction. If not, the party perceiving to receive significantly less value for the exchanged object, for example, than the price paid,  
      The fairness of a transaction may be influenced, often significantly, by subjective trading factors outside the knowledge of one party or the other. Frequently, subjective factors are used to determine whether the trading parties find enough parity in the terms of the trade to allow a deal to move forward to completion. A transaction is likely to proceed, where there is some degree of parity in the values of the objects sought to be exchanged. An exchange that is deemed to be a roughly even trade is deemed to be fair, but only after protracted negotiations to achieved an acceptable degree of parity. On the other hand, transaction believed to be very favorable to a party, may lead that party to instinctively and quickly agree to the expressed terms, eliminating further negotiation. For example, if a buyer obtains a desired object at a price lower than the price identified by the buyer as the point of parity, then the buyer would consider the trade to be a “good” deal. If the offered price is well below the buyer&#39;s point of parity, or a subjective factor known to the buyer indicates that there is additional, unobvious value to be gained in the trade, the buyer may deem the deal to be a “great” deal, that is, a bargain. Unknown and subjective factors may facilitate an individual deal but, overall, such factors may impede trade.  
      For transacting parties, it is desirable for each to have information about the other, and about the object of trade. A decision by a transacting party to accept the validity of the information about the other party, and the transaction, can be expressed as trust. Two parties who trust each other are more likely to complete a transaction quickly. The buyer&#39;s trust in the seller indicates the buyer&#39;s belief that the seller is not misrepresenting trade intentions, price, or trade object values. A seller&#39;s trust in the buyer indicates that the seller believes that the buyer will tender payment of the agreed-upon price, on the terms promised. Buyers and sellers who engage in series of “good” or “fair” deals tend to return to each other for additional transactions. If a party considers the other as untrustworthy, or as one who is not fair or willing to give a good deal, then the party becomes disinclined to deal with the “unfair” other.  
      The acts of third parties may skew, distort, or corrupt one or more transactions, which when discovered, tend to dissuade the transactors from executing a trade. If the method by which a seller executes transactions is untrustworthy, that is, can be corrupted or manipulated by third parties, buyers are unlikely to return in the future to engage in commerce with that seller. Typically, it is in the best interests of both parties to engage in fair transactions, and to use trustworthy methods of transactions.  
      As the nature of transactions becomes more complex, buyers and sellers both tend to seek out the most trustworthy trading partners with whom to do business. Trust, then can improve trading relationships among parties, and can provide an environment supportive to the execution of efficient transactions.  
      Transactions often involve more than just one buyer and one seller. Such transactions may introduce a competitive element into the relationship between a seller and a buyer. In one form of competitive transaction, two or more buyers compete to offer to the seller, i.e., bid, the highest price that the respective buyer is willing to pay for the object. A seller may offer an object to the buyers at an established price. One buyer may place a bid for the object at or above the established price, intending to buy the object. The seller may accept the offered bid, or indicate a desire to receive a higher bid by asking a higher price. Another buyer, who may place a higher value on the object than the first buyer, often places a bid representing a willingness to pay that higher price. Again, the seller may accept this bid, or may solicit a higher bid by raising the asking price. Again, either previous bidder, or another buyer may place a bid corresponding to the higher asking price. Again, the seller may accept or reject this new bid. The process of ask and bid repeats until the buyers indicate an unwillingness to buy at the current asking price. Usually, the seller will conclude the transaction by accepting the highest accepted bid, after which the successful buyer makes payment or agrees to make payment, to receive the object. In this scenario, termed a forward auction, the buyers are offerors who place bids, which individually represent the price that respective buyers are willing to pay for an object. In general, the bids are made such that the bid price increases monotonically during the evolution of the auction. The price paid by the buyer is usually higher than the initial established price, or the first bid.  
      Some auctions may reverse the roles of offeror and offeree. For example, in a reverse auction, the seller is the offeror, stating an initial maximum offer price for an object. Here, it is the buyers who either accept or reject the offer. If the buyers reject the seller&#39;s offer, or if additional inventory must be sold, the seller states a new, lower offer price for the objects. Again, buyers may accept or reject the offer. A seller may repeat the process of sequentially decreasing offer prices until inventory is depleted. Although this method gives buyers the incentive to wait until the seller offers the lowest possible price, the buyers usually know that the objects being auctioned are considered to be scarce and needed. Generally, demand increases as prices decline. As the reverse auction progresses, the seller&#39;s inventory tends to dwindle. A decision to delay accepting the seller&#39;s offer at a given price is made at the peril of the seller&#39;s inventory being exhausted before the reluctant buyer secures the desired number of objects. Typically, the price paid for an object during a reverse auction is lower than the initial offer price. When a buyer agrees to a trade, the price paid is usually higher than the final price that will be paid by the final buyer. Thus, a buyer must balance the desire to buy at the lowest desired price against the reality of an increase in demand, and inventory exhaustion, before the lowest desired price is reached.  
      There are myriad types of transaction systems used for commercial exchanges, including those undertaken for public utility resource allocation, for institutional purchases, for routine commercial exchanges, and even for personal enjoyment. Auctions, bazaars, swaps, barter exchanges, and similar transactions involving negotiations and structured exchange protocols, are among the most popular transaction systems at nearly every level of exchange. These systems meet the need for buyer and seller to interact, often in real time, to assure that each meets their expectations for the desired bargain. Despite the convenience of established transactions, some buyers may desire a transaction system that offers opportunities to effect exchanges with a degree of excitement, spirited exchange, and an illusion of risk, without the actual risk usually associated with gaming systems and games of chance and luck.  
      As noted above, a buyer must place some degree of trust is in the buyer and in the transaction method. For example, the buyer must trust the seller to accurately represent the goods offered for sale and to surrender purchased goods to the buyer, as promised. The seller must trust the buyer to surrender the agreed-upon amount of money, or an object of comparable value, in exchange for the object exchanged. Both seller and buyer place some trust in the system by which the transaction is executed. On one hand, the buyer must trust that the seller has not introduced persons or techniques that place undue influence on transactions, perhaps causing the buyer to pay more for an object than would otherwise be paid. On the other, the seller must trust that there is no collusion among buyers to manipulate the transaction system to unduly influence transactions to the detriment of the seller. Similarly, a buyer must trust that the transaction system may not be manipulated by the seller and another potential buyer, or by a group of colluding buyers, to distort the transactional process.  
      Even when both buyer and seller have well-founded trust in each other, and in the transactional system to be used to effect their commercial exchange, the system may be at risk from unscrupulous parties who seek to exploit weaknesses in the transactional process to their advantage and gain. Some exploiters may use purloined historical, demographical, or personal information about the buyer or seller to siphon profits from the transaction profits. Others may surreptitiously monitor the transaction system to identify trade correlations and predict future prices or transaction trends, allowing the exploiter to cash in on the illicit knowledge. Such disreputable practices can be especially burdensome for many types of transactions.  
      For example, in highly-structured negotiations, such as auctions, process subversion, shilling, price and value manipulation, and other fraudulent, collusive, predatory, or entry-deterring behavior can substantially reduce the efficiency, fairness, and simplicity of the negotiations, particularly for recurring or parallel negotiations. A venue, in which such undesirable activities were perceived to hold sway, is likely to experience reduced profitability and loss of target clientele.  
      Perhaps more significantly, transactions which may be perceived as based on a potentially corruptible and unfair process, or as suitable only for those with special knowledge or skills, may discourage a substantial population of potential participants from engaging in those transactions. Unfortunately, market goers who are vexed and dissatisfied with explicit and implicit collusion, shilling, process manipulation, and the like, in online auctions, bazaars, swap sites, and other popular marketplaces may rarely, if ever, return. Additionally, costly measures such as conduct policing systems and reputational screening may be need to preserve an acceptable degree of integrity in the operation.  
      Nevertheless, motivated observers may seek unfair advantage, relevant information regarding a transaction, or class of transactions, as well as the corresponding transactional process. Skilled analysis of past process performance, as well as of the signals used during negotiations, also may permit the analyst to expressly or implicitly distort the transaction process and outcomes to an unfair advantage. Despite certain safeguards, unscrupulous conduct may be encouraged, before or during a transaction, by the open availability of information characterizing the trade object to be transacted; the trade object pricing, value, and authenticity; the transaction participants, and their likely behavior; the economic environment of the transaction, including financial state of the seller, broker, or both; as well as other uncovered private information relevant to the transaction. This information then may be used to unfairly extract significant profits for the dishonest actor.  
      It is desirable therefore, to provide a transaction system that minimizes, if not eliminates, the influence of collusion, unfair price manipulation, or other process corruption by unscrupulous parties. It also is desirable to provide a transaction system that, when adapted to do so, may provide a degree of excitement and spirited exchange, which may also exhibit an illusion of risk.  
     SUMMARY OF THE INVENTION  
      The present invention satisfies at least the aforementioned needs, and others known to the field of transaction or trading systems by providing a trading system, including a vendor disposed to propose an object offer at an offer value; a vendee disposed to accept the object offer at a purchase value; and a communication link coupling the vendor and the vendee, by which the vendor and the vendee communicate object offer data. The object offer data includes a stochastic tuple related to the offer value. In accordance with the practice herein, the vendor proposes the object offer to the vendee through the communication link such that the vendee is induced to accept the object offer when the offer value is one of generally equal to and less than the purchase value.  
      The stochastic tuple includes a proposed offer value and an offer interval, with one or both of the proposed offer value and the offer interval being a stochastic variable value. Furthermore, aspects of the invention herein provide a sequence of stochastic tuples communicated by the vendor to the vendee during a defined transaction period. The object offer represents one of a product, a service, and a combination thereof. In certain embodiments, the vendor proposes the object offer within a preselected marketing schema chosen to entice the vendee to accept the object offer of the vendor. In selected ones of these embodiments, the preselected marketing schema comprises an interactive, multimedia entertainment schema.  
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
      The invention may be better understood, and further advantages and uses thereof made more readily apparent, when considered in view of the following detailed description of exemplary embodiments taken with the drawings in which:  
       FIG. 1  is a diagrammatic representation of an adaptive stochastic transaction system embodiment, according to the present invention;  
       FIG. 2  is a diagrammatic representation of an exemplary embodiment of an adaptive marketing module with stochastic data, according to the present invention;  
       FIG. 3  is a diagrammatic representation of data sequence corresponding to a stochastic process producing variable offer values as applied to inventive systems and modules herein;  
       FIG. 4  is a diagrammatic representation of data sequence corresponding to a stochastic process producing variable offer values and corresponding variable offer intervals as applied to inventive systems and modules herein;  
       FIG. 5  is a diagrammatic representation of data sequence corresponding to an adaptive stochastic process employing multiple selected variable offer values and corresponding variable offer intervals, as applied to inventive systems and modules herein;  
       FIG. 6  is an embodiment of an adaptive stochastic transaction system having an apparatus capable of generating a data sequence as illustrated in  FIG. 3 ;  
       FIG. 7  is an embodiment of an adaptive stochastic transaction system having an apparatus capable of generating a data sequence as illustrated in  FIG. 4 ;  
       FIG. 8  is an embodiment of an adaptive stochastic transaction system having an apparatus capable of generating a data sequence as illustrated in  FIG. 5 ;  
       FIG. 9  is an embodiment of a graphical user interface, which may be presented and perceived by a prospective buyer, using selected embodiments of the present transaction;  
       FIG. 10  is an illustration of certain embodiments of the inventive transaction system in the context of a commercial enterprise; and  
       FIG. 11  is a diagrammatic representation of data sequence corresponding to an adaptive stochastic process employing selected variable offer values and corresponding variable inventory intervals, as applied to inventive systems and modules herein.  
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS  
      Embodiments of the present invention encompass an adaptive stochastic transaction system, method, and computer-readable article of manufacture, in which one entity is constituted to communicate, over a communication route, a stochastic decision token to at least one second entity, with the intention of inducing the at least one second entity to respond with a desired behavior to the stochastic decision token. The behavior can include the second entity responding to the stochastic decision token with a corresponding response token.  
      A transaction can describe a unit of exchange between the entities and may include a signaling protocol by which the entities indicate their respective transaction intentions. By means of a transaction, the signaling entities exchange a trade object for a trade value. In general, a trade object may be a product, a service, an asset, a resource, an allocation, or an equivalent, as well as a combination thereof. A trade value can be represented by another object, or by an agreed quantity of a defined medium of exchange (DME). In a commercial context, an example of a DME is cash. A transaction may be an actual exchange, or may be a commitment to exchange. In the latter case, the actual exchange is initially deferred and later completed by one or more ancillary communications or transfers. However, any tangible or intangible item, token, property, symbol, or trade object may represent a DME unit. Thus, DME may be represented by bandwidth, priority, power, access, tenure, or whatever other dimension transacting entities may deem as an acceptable DME.  
      As used herein, the term dimension is not limited to any of the three measures of length, breadth and height. Instead, as used herein, a dimension is a construct, scale, or categorization, describing a broad grouping of descriptive and potentially varying, data, or a state of being, whereby objects or individuals can be distinguished. As such, a dimension may include a construct, scale, or categorization, that is fundamental, is derived, or is a combination thereof; and which may be expressed, for example, in absolute, relative, or differential terms. Familiar examples of a dimension are time or length, which may be expressed respectively as a time of day or distance, a time or length offset, and time or length interval. By extension, an exemplary derived or combined dimension can be speed, derived from traversing an interval of length during an interval of time; or can be acceleration, derived from a difference in speed during an interval of time. Another non-limiting example of a dimension may include an absolute value or price; a relative value or price offset; or a difference in value or price. By extension, a dimension also may be price or price difference expressed as a function of time or time difference; of product inventory level or level change; of margin or margin difference; of sales volume or sales volume change; of bandwidth or bandwidth change; of a customer response, or demographic or market datum; of at least one preselected competitive enterprise indicators; and so on, whether alone or in combination. Where useful for exposition, the term, trade dimension, may be used, and is to be considered synonymous with other uses of the term, dimension.  
      A stochastic decision token includes at least one dimension representative of a trade object, which demonstrates stochastic characteristics over a domain, within in a range, or both. In general, a “stochastic” characteristic is one that is non-deterministic, and can be described, at least in pertinent part, by the laws of probability. That is, the dimension characteristics may be generated such that the next state of the dimension tends not to be fully determined by its previous state. For clarity, “stochastic” will be synonymous with “random,” encompassing the entire domain of non-deterministic features including, without limitation, stochastic and pseudo-random features, as well as stochastic and random features.  
      A single non-deterministic variable often is termed a random, or randomized, variable, with an ordered collection, or sequence, of random variables being called stochastic process. A stochastic dimension may be formed of a randomized portion alone, or of a randomized portion in combination with a deterministic portion. Although a future value of a stochastic sequence may not be ascertainable from previous values, a sequence may be devised to reflect a preselected mean and a preselected variance, with values being relatively dispersed within a preselected distribution envelope. Nevertheless, the randomized nature of the dimension can be preserved, even if a deterministic portion of a stochastic variable representing that dimension may be measured, and the corresponding mean value, variance, and distribution function can be ascertained. Within some contexts, metrics corresponding to a desired behavior may be described in terms of risk-taking, efficiency, error, Shannon entropy, and the like.  
      The first entity may adapt aspects of the system response to the behavior of the second entity, as well as to systemic factors. For example, in response to observed or anticipated behavior by the second entity, the first entity may modify the categories and quantity of trade objects available for exchange, modify access to transactions, manage information pertinent to transactions and trade objects, or shape DME-related, stochastically-derived, trade object attributes by selectively modifying a preselected stochastic process. Therefore, embodiments of transaction systems according to the teachings of the present invention can be configured to be self-adjusting, adaptive transaction systems.  
      Also, a communications route may be formed from at least one communications channel, which communications channel may be formed from at least one communications path. In turn, a communications path may be formed from at least one communication link. Each communications link includes at least one circuit, which serves as a medium for transferring information. This medium may transport information in analog or in digital form, using wired or wireless signal propagation techniques to carry information. The information may be conveyed by multiple communications formats and communications protocols. Therefore, a communication route may be capable of conveying information using, alone or in an operable combination, multiple communication channels and media, multiple signal propagation techniques, and multiple communications formats and communications protocols. Although bidirectional communication between parties is desirable, a communication effected in one direction between parties is not required to employ the same or similar channel, media, signal propagation technique, communications format, or communications protocol to effect a communication in any other direction.  
      Advantageously, features, aspects, and embodiments of the present invention may be disposed to provide a myriad of realized outcomes for the transacting parties. As used herein, the term “business operator” may include an enterprise, or back-office, executive, a seller, or both. In selected generalized implementations, a business operator may use multiple sellers and multiple types of trade objects during the course of enterprise operations.  
      Of course, in this context, the notion of business operator encompasses an apparatus which includes, without limitation, one or more of computing, sensing, communication, and networking subunits. A business operator also can be embodied in computer code embodied on a computer-readable medium that, when executed on a computing apparatus, causes the computer apparatus to perform an adaptive, stochastic transaction process, according to principles taught and described herein.  
      As intended herein, a business operator can receive information and business intelligence in the form of selected trade indicators and, responsive to those selected trade indicators, adapt business operations to the realities of both market and operational realities and events, in real-time or near-real time. The selected trade indicators can be drawn from any source within or surrounding the enterprise, which may be indicative of a market trend or circumstance important to the business owner. In many instances, a selected trade indicator may be related to one or more of the aforementioned trade dimensions.  
      An exemplary selected trade indicator may include, without limitation and alone or in combination: a trade object inventory, a trade object purchase price, a trade object availability, a trade object delivery, and trade object vendor selection and payments; a credit factor or a financing factor for the operation, a business operator, a seller, a vendor, or a buyer; measured or estimated buyer interest in one or more selected trade objects, purchasing trends, and buyer behavioral tendencies; geographic, regional, seasonal, temporal, and demographic factors; and buyer responses to trade object brands, terms of trade, seller styles and personalities, and so on.  
      Moreover, where a buyer is set off from the business operator, and effecting trade through a communications device or system, such as a telephone network or a public internetwork, exemplary selected trade indicators may include, without limitation and alone or in combination: telephone call volume, network bandwidth consumption, completed internetwork links, actual sales volume, volume of non-sale inquiries or comments, buyer responses to sales incentives, and the like.  
      A selected trade indicator may be one or more ratiometric and comparative measures of buyer interest, purchasing desire, and market conditions, such as a telephonic sale to telephonic contact ratio, an internetwork-related sales to total internetwork-related link ratio; a telephonic sales volume to internetwork sales volume ratio; contact and sales volume comparisons between and among geographic, demographic, special interest, collectors, and other real or virtual self-selected groups.  
      In general, then, a business operator may employ as a selected trade indicator as many or as few direct or indirect measures of buyer activity and behavioral predictors, geopolitical, socioeconomic and other quantifiable measures of trading activity, again, alone or in combination. A selected trade indicator may also be a combination of multiple other selected trade indicators, which may be combined linearly, non-linearly, or in combination.  
      Some embodiments of an adaptive stochastic transaction system may be configured to bias the adaptation of a process recited herein to a particular business outcome in favor of a seller; in certain instances, an improvement in the outcome realized by a seller is achieved at the expense of a buyer. If that expense is too great, the buyer may conclude that they overpaid for the trade object and did not receive a fair deal. The buyer tends to be discouraged from future transactions with that seller, because of the perceived negative transaction experience.  
      Other embodiments may be configured to bias adaptation of a process recited herein to a particular business outcome in favor of a buyer; in certain other instances, an improvement in the outcome realized by the buyer is achieved at the expense of the seller. For example, a seller may find necessity to reduce excess inventory at a substantial loss, and conclude that they ought not to continue offering the discounted trade object. The seller tends to be discouraged from future transactions with that buyer, also because of the perceived negative transaction experience.  
      Pragmatically, it is possible and often desirable, to provide selected embodiments of the present invention adapted to offer a win-win outcome to both transacting parties, akin to Pareto efficiency. In general, the perceived transaction experiences of both the seller and the buyer are positive with a perception of fair and successful dealing being held by both the seller and the buyer.  
      Adaptation can evolve from selected trade indicators, which provide the seller with relevant information and intelligence regarding the processes pertaining to the business operator&#39;s enterprise. A business operator may use selected trade indicators to adjust an adaptive stochastic transaction process herein to meet desired business objectives and to influence the behavior of the buyer in real-time, near-real-time, periodically, or episodically.  
      Adaptation also can evolve from a judgment action taken by the seller. A judgment action is a manual input which may be responsive to a selected trade indicator, or imposed by a human operator, in a manner that may appear “arbitrary.” However, such a judgment action can arise from a choice by the human operator that is generally intuitive and thus typically not measurable in traditional terms.  
      Turning now to the Figures,  FIG. 1  represents an exemplary embodiment of adaptive, stochastic transaction system  100 . Communications proceed by signaling according to a preselected transaction protocol, with respect to a defined transaction. The defined transaction can be a predefined trading event, conducted over a predefined trading interval. In system  100 , first transactor T 1    110  signals at least one stochastic decision token ψ  160 , to second transactor T 2    120 ; and is connectable with second transactor T 2    120  through communication route  130 , to so communicate. Communication route  130  typically includes uplink  140  and downlink  150 . In general, once it is communicated from first transactor T 1    110  over downlink  150  and perceived by second transactor T 2    120 , stochastic decision token ψ  160  is disposed to induce an observed behavior in second transactor T 2    120 . Stochastic decision token ψ  160  can be representative of a trade value presently associated with the preselected trade object (not shown), which is subject to the present transaction. In view of the stochastic nature of the trade value associated with stochastic decision token ψ  160 , future trade values may be difficult to predict on the basis of past values. This property may be perceived as an element of risk.  
      Although difficult prediction of future values, and financial risks, may be undesirable to some persons in other types of transactions, it can be desirable in the context of the present invention, because it is well-known that small risks of many types can be both stimulating and enjoyable for many individuals except, perhaps, for the most risk-averse. Therefore, the stochastic characteristics as employed, for example, in transaction systems according to the present invention, may be affectively stimulating and enjoyable, particularly if the transaction system is embodied within an entertainment milieu.  
       FIG. 2  illustrates business-to-consumer enterprise system  200 , which can be similar to adaptive, stochastic transaction system  100 , described in  FIG. 1 . Enterprise system  200  includes enterprise host module  205  (i.e., seller  205 ), which is coupled to bidirectional communication channel  207 , and which thereby can connect to at least one consumer module  210  (i.e., buyer  210 ). When connected through channel  207 , seller  205  and buyer  210  may engage in a transaction for one or more preselected trade objects using a preselected trade protocol. Channel  207  can include at least uplink  215  and downlink  220 , and it may be desirable that one or more selected links in communication route  207  be a multimodal, bidirectional communication channel, capable of multimedia transmissions and, further, of one or more of asynchronous, isochronous, broadcast, or multicast, communications, using wired and wireless signal communication techniques.  
      Further, communication route  207  can provide one or more communication links that traverse a point-to-point communication network, a circuit-switched communication network, a store-and-forward communication network, a packet-switched communication network, a broadcast communication network, and a combination thereof. An exemplary communication network presently having store-and-forward and packet-switched features, with quality-of-service-aware capabilities (e.g., isochronous, asynchronous, etc.), may include a packet-switched communications internetwork, such as the Internet. Another type of communication network, the public switched telephone network, is an example of a circuit-switched network facilitating point-to-point communications. Likewise, an interactive producer-to-consumer satellite-based broadcast network may exemplify an exemplary broadcast communication network, which also include a cable-access (CATV) link. Furthermore, present wireless mobile communication devices enable hand-held multimedia communication with text messaging, video, audio, and stored program features.  
      Thus, although communication route  207  may employ a single mode and class of communication network, or link, is within the scope of the present invention that communication between parties may be accomplished using multiple modes, links, and classes of communications entities. For example, the communication path and nature of components constituting uplink  215  may be distinct from those constituting downlink  220 . Indeed, in selected embodiments of the present invention, at least a portion of uplink  215  may include a broadcast network, by which a video presentation of a transaction is televised from seller  205  to buyer  210 . In addition, at least a portion of downlink  220  may include a computer internetwork, such as the Internet, or a public telephone network, by which buyer  210  may respond to a televised presentation by seller  205 .  
      While in  FIG. 1 , first transactor T 1    110  signals at least one stochastic decision token ψ  160 , to second transactor T 2    120 , in  FIG. 2 , seller  205  is disposed to signal at least one stochastic decision tuple  225  to buyer  210  through downlink  215 . As before, seller  205  signals buyer  210  with a query described by stochastic decision tuple  225 , with the intention of inducing buyer  210  to respond to stochastic tuple  225  with a desired behavior. In general, once perceived by buyer  210 , stochastic decision tuple  225  is disposed to induce an observed behavior in buyer  210 , including a response to seller  205 . Desirably, stochastic decision tuple  225  is an ordered set of one or more dimensions associated with an intended transaction between seller  205  and buyer  210 . At least a portion of one dimension is generated by buyer  205  as a stochastic portion, as indicated previously.  
      Stochastic decision tuple  225  may be, for example, a singleton or a duplet, which are sets having one element and two elements, respectively. An exemplary singleton may contain an element or dimension, which is stochastic in part or in whole. For example, offer value ρ  235 , can be generated from a base value, which is summed with a randomized value, and can be representative of a trade value associated with the preselected trade object (not shown) presently being transacted. An exemplary duplet may contain two dimensions, for example, offer value ρ  235  and offer interval δ  230 , at least one of which being. stochastic in part, or in total. Tuple  225  also may include three or more values, at least one of which also being stochastic in nature.  
      Although tuple  225  may contain multiple dimensions of information, it nevertheless can be adapted to form a compact token, as may be desirable to minimize the resources used to facilitate one-to-many transmission, such as transmission time and power, channel capacity, bandwidth, and so on. Thus, whether seller  205  is connected simultaneously through channel  207  to one buyer  210 , or to one hundred thousand buyers  210 , it may be sufficient to simultaneously query buyer(s)  210  with one stochastic decision tuple  225 .  
      For clarity, stochastic decision tuple  225  is described in terms of a stochastic two-element set &lt;δ,ρ&gt;. Set element δ  230  can be representative of an offer interval, or the time over which a corresponding offer value may be considered valid. That is, upon expiration of offer interval δ  230 , paired offer value ρ  235  is revoked. Similarly, set element ρ  235  can be representative of an offer value, or present stated cost for a trade object. Also, where offer tuple  225  is one of an ordered sequence of stochastic tuples signaled over time to buyer  210 , interval δ  230  and offer value ρ  235  can be indexed to their respective order in the associated time sequence, such that tuple  225  can be symbolized by &lt;δ i ,ρ i &gt;. One or both of offer interval δ i    230  and offer value ρ i    235  can be stochastic. However, when only one element of a duplet  225  is stochastic, it is desirable that offer value ρ i    235  be randomized.  
      In certain embodiments, the preselected trade protocol describes a trading event during which a preselected trade object may be offered to buyer  210 . The span of a trading event can be subject to one or more limitations, such as a predefined trading interval Δ, a preselected trade object count and so forth. A predefined trade object count can be a trading event inventory (i.e., the maximum number of trade objects allocated for a given trading event), or a total trade object inventory (i.e., the maximum number of trade objects available for allocation).  
      Typically, the span of a trading event Δ N  can be described in terms of the time represented by the maximum number N of predefined offer intervals allocated to the trading event. For example, if the maximum span of trading interval Δ encompasses N offer intervals δ i    230 , then trading interval Δ N  may be described as the sum of N offer intervals δ i    230 . Symbolically:  
       Δ   =       ∑     i   =   1     N     ⁢           ⁢     ∂   i           
 
      Ordinarily, seller  205  signals stochastic tuple &lt;δ i ,ρ i &gt;.  225  to buyer  210  prior to the an i th  offer interval, for example, during the (i−1) th  offer interval, thereby indicating that the i th  offer interval will have a duration of δ i , during which the preselected trade object will be offered at a offer value of ρ i . When ρ i  is generated as a stochastic variable, the offer values ρ 1 , ρ 2 , . . . , ρ N  can be perceived by buyer  210  as varying randomly, even if within a predefined range of values. Moreover, offer values ρ 1 , ρ 2 , . . . , ρ N  also may appear to be generally random and uncorrelated to an unscrupulous observer attempting to manipulate future offer values of a trading event on the basis of past values or to otherwise use process, participant, or trade object information to subvert the commercial process evolving between seller  205  and buyer  210 . Such disreputable practices can be especially burdensome for some types of transactions.  
      For example, in highly-structured negotiations, such as auctions, process subversion, shilling, price and value manipulation, and other fraudulent, collusive, predatory, or entry-deterring behavior can substantially reduce the efficiency, fairness, and simplicity of the negotiations, particularly for recurring or parallel negotiations. A venue in which such undesirable activities were perceived to hold sway, is likely to experience reduced profitability and loss of target clientele.  
      Perhaps more significantly, transactions which may be perceived as based on a potentially corruptible and unfair process, or as suitable only for those with special knowledge or skills, may discourage a substantial population of potential participants from engaging in those transactions. Unfortunately, market goers who are vexed and dissatisfied with explicit and implicit collusion, shilling, process manipulation, and the like, in online auctions, bazaars, swap sites, and other popular marketplaces may rarely, if ever, return. Additionally, costly measures such as conduct policing systems and reputational screening may be needed to preserve an acceptable degree of integrity in the operation.  
      Nevertheless, motivated observers may seek unfair advantage, relevant information regarding a transaction, or class of transactions, as well as the corresponding transactional process. Skilled analysis of past process performance, as well as of the signals used during negotiations, also may permit the analyst to expressly or implicitly distort the transaction process and outcomes to an unfair advantage. Despite certain safeguards, unscrupulous conduct may be encouraged, before or during a transaction, by the open availability of information characterizing the trade object to be transacted; the trade object pricing, value, and authenticity; the transaction participants, and their likely behavior; the economic environment of the transaction, including financial state of the seller, broker, or both; as well as other uncovered private information relevant to the transaction. This information then may be used to unfairly extract significant profits for the dishonest actor.  
      Thus, the use of stochastic decision tuple  225  can be a desirable transactional signaling device, because an observer of a stochastic process may not be able to predict, with a reasonable degree of certainty, a future value of a randomized element from a previous value, even if general characteristics of the process are known or can be determined. As a result, stochastic transaction signaling according to the embodiments herein, provides an elegant, effective barrier to process subversion, collusion, and similar undesirable influences, because of the onus of extracting timely, useful information from the stochastic transaction signals, which seller  205  communicates to buyer  210 .  
      Generally, one aspect of the preselected trading protocol involves seller  205  signaling buyer  210  with stochastic decision tuple &lt;δ i ,ρ i &gt;  225  prior to the beginning of the i th  period of trading interval Δ N . Dimension δ i    230  represents the duration of i th  period of trading interval Δ N . Although trading interval Δ N , may be predefined, it also may be determinable by a seller. Of course, a buyer may terminate involvement in a trade by discontinuing involvement in the trade. Trade will continue if other buyers are participating in the trade, and sufficient inventory is available. Dimension ρ i    235  represents the offer value to be asserted during the i th  offer interval.  
      Thus, stochastic decision tuple &lt;δ i ,ρ i &gt;  225  is representative both of a time dimension and a cost/price dimension, and is a signal to buyer  210  from seller  205  that, starting from the beginning of the i th  period and lasting only for an interval of δ i    230 , buyer  210  may take the trade object of the transaction at a value of ρ i    235 . However, after offer interval δ i    230  elapses, the offer value of ρ i    235  is revoked and invalid. Should buyer  210  wish to take the trade object, the next opportunity to do so will occur during the (i+1) th  period of trading interval Δ N , with subsequent stochastic decision tuple &lt;δ i+1 ,ρ i+1 &gt;  225  describing subsequent offer value ρ i+1    235  and the subsequent offer interval δ i+1    230  during which offer value ρ i+1    235  will be considered to be valid. In general, if ρ is a stochastic dimension, then the magnitude of offer value ρ i+1  may be greater than, less than, or equal to, the magnitude of offer value ρ i , ρ i+2 , or any other offer value in the sequence of offer values presented to buyer  210  during the subject trading event. A graphical representation of a time-domain mapping of a trading event will be illustrated in  FIG. 3 , in which seller  205  signals buyer  210  with tuple  225  bearing stochastic offer value ρ  235  and deterministic offer interval δ  230 . Graphical representations of trading events in which seller  205  signals buyer  210  with tuple  225  bearing both stochastic offer interval δ  230  and stochastic offer value ρ  235  will be illustrated in  FIG. 4  and  FIG. 5 .  
      Relative to one embodiment of a preselected trading protocol employed in system  200 , buyer  210  may initiate communication with seller  205  through uplink  220  of channel  207 , expressing an intention to engage in a mutually beneficial exchange, or a trade. Seller  205  then can signal stochastic decision tuple &lt;δ i ,ρ i &gt;  225  to buyer  210  for evaluation and response. After perceiving the information received from seller  205  in stochastic decision tuple &lt;δ i ,ρ i &gt;  225 , buyer  210  can signal seller  205  with response token  240 . Typically, buyer can assign preselected response values to response token  240 , as described under the preselected trading protocol. For example, response token  240  can be assigned a response value of COMMIT Π i    245 , or CANCEL X  250 . Desirably, COMMIT response Π i    245  can be linked, for example, using index i, to corresponding offer interval δ i    230  and corresponding stochastic offer value ρ i    235 , to verify that buyer  210  is responding to the present values, which also can be linked, for example, using index i. Conveniently, NULL response Ø  255  can cause a default value of REJECT to be assigned to token  240 . Thus, by not responding within a period described by the preselected trading protocol (typically, the offer interval δ i ), seller  205  may assume that buyer  205  declined, or rejected, the offer to trade during the i th  offer interval δ i , at the i th  offer value ρ i . Desirably, the preselected trading protocol instructs buyer  210  to make an affirmative act, in order to signal seller  205 . For example, with a COMMIT Π i  response  245  being assigned to token  240 , buyer  210  makes a commitment to seller  205 , during offer interval δ i , to exchange for the preselected trade object, an in the amount of DME equivalent to offer value ρ i , by which commitment a transaction is made. Also, seller  205  may permit buyer  210  to issue a CANCEL X response  250 , by which a made transaction subsequently is repudiated. In this particular embodiment, both COMMIT Π i  or CANCEL X responses are accomplished by affirmative steps of buyer  210 , which can lessen the likelihood of spurious transactions. Unless buyer  210  disconnects from uplink  220 , the trade object inventory is exhausted, or trade interval Δ N  has elapsed, seller  205  can be disposed to signal another stochastic decision tuple &lt;δ i+1 ,ρ i+1 &gt;  225  to buyer  210 . Although trading interval Δ N , may be predefined, it also may be determinable by a seller. Of course, a buyer may terminate involvement in a trade by discontinuing involvement in the trade. Trade will continue if other buyers are participating in the trade, and sufficient inventory is available.  
      To seller  205 , the preselected trading protocol includes signaling buyer  210  with stochastic decision tuple &lt;δ i ,ρ i &gt;  225 , waiting for a predefined decision period, e.g., offer interval δ i , the receipt of response token  240  from buyer  210 . Thus, a simple model of transaction communication in system  200  is one of query between seller  205  and buyer  210  over downlink  215 , and response between buyer  210  and seller  205  over uplink  220 . In this model, a query may be in the form of tuple  225  and a response may be in the form of token  240 .  
      If, during offer interval δ i , buyer  210  signals seller  205  with token  240  bearing COMMIT value  245 , then seller  205  makes the transaction with buyer  210 . If, after making the transaction, buyer  210  signals with token  240  bearing CANCEL X, then seller  205  cancels the transaction with buyer  210 . Unless the trading event has ended, seller  205  can repeat the query by signaling buyer  210  with next stochastic decision tuple &lt;δ i+1 ,ρ i+1 &gt;  225 . Alternately, to avoid the costs of canceling a made transaction, seller  205  may defer finalization of transactions (making and canceling) until the close of the trading event. However, from the perspective of the buyer, issuing a COMMIT response token  240  to seller  205  may be regarded as a non-contingent transaction, cancelable at the discretion of seller  205 , and not as a matter of protocol, as with other classes of transactions, such as auctions or speculation buys. In other words, by communicating a COMMIT response token  240 , the buyer affirms a willingness to accept the offered trade object during the selected offer interval. It may be beneficial to seller  205  to permit buyer  210  to freely cancel a transaction, however, due to the higher costs related to returned orders, refunds, credit card transaction corrections, restocking, and so on. Therefore, buyer  210  may be provided a mechanism, e.g., a CANCEL,.X, by which buyer  210  may rescind an accepted offer, before the completion of the respective trading event.  
      From the perspective of buyer  210 , one embodiment of a preselected trade protocol can include connecting with seller  205  via uplink  220  and request access to a predefined trading event for a preselected trade object. If access is granted, buyer  210  is queried by stochastic decision tuple &lt;δ i ,ρ i &gt;  225  from seller  205 . By perceiving the information in stochastic decision tuple &lt;δ i ,ρ i &gt;  225 , buyer  210  understands that the preselected trade object can be obtained at offer value ρ i , with the offer being valid only for the remaining duration of offer interval δ i . If buyer  210  elects not to make the transaction under those terms, perhaps with the hope that a future offer value, such as offer value ρ i+1  will be less than offer value ρ i , perhaps significantly less, then buyer  205  will allow offer interval δ i  to elapse without action. Of course, due to the stochastic nature of at least one dimension (here, ρ i ) of tuple  225 , the magnitude of future offer value ρ i+1  may be greater than, equal to, or less than, the magnitude of current offer value ρ i . By not responding to seller  205  within offer interval δ i , buyer  210  has constructively rejected the offer from seller  205  to make a trade for the preselected trade object at offer value ρ i .  
      Upon, or shortly before, the expiration of offer interval δ i , but before the end of trading interval Δ N , buyer  210  can be queried again by receiving stochastic decision tuple &lt;δ i+1 ,ρ i+1 &gt;  225  for evaluation and response. Should buyer  210  elect to make a trade for the trade object subject to the trading event—at offer value ρ i+1 , it is desirable that buyer  210  assign a value of COMMIT Π i+1    245  to token  240  and respond with token  240  so that it is received by seller  205 , before the expiration of offer interval δ i+1 . Upon receipt of the COMMIT Π i+1    245  response from buyer  210 , seller  205  can proceed to make the requested transaction, using offer value of ρ i+1    235  as the trading price. Should buyer  210  hesitate in taking the present offer of seller  205 , and seller  205  does not receive token  240 , bearing the COMMIT response Π i+1    245 , before offer interval δ i+1  elapses, the effect can be that of NULL Ø response  255 , i.e., a default REJECT response. If buyer  210 , after making a trade with seller  205  during offer interval δ i+1 , decides that continuing with the transaction is undesirable, buyer  210  may signal with response token  240  bearing a CANCEL value X. Although trading interval Δ N , may be predefined, it also may be determinable by a seller. Of course, a buyer may terminate involvement in a trade by discontinuing involvement in the trade. Trade will continue if other buyers are participating in the trade, and sufficient inventory is available.  
      To illustrate the expressed operational principles therein,  FIG. 3 ,  FIG. 4 , and  FIG. 5 , make appropriate reference to aspects of system  200  in  FIG. 2 . Nevertheless, neither system  200 , nor the expressed operational principles illustrated through reference to  FIGS. 3-5  should be taken to be so limited. The principles thus exposited, and implied, also are generally in accord with principles corresponding to the function and operation of generalized transaction system  100  in  FIG. 1 .  
       FIG. 3  is a mapping representative of possible outcomes of stochastic dimension process (generally at  300 ), which may be used to generate stochastic decision tuple sequence &lt;δ,ρ&gt;. For clarity, the mapping of process  300  is two-dimensional, within the time domain (x-axis) and a “price” range (γ-axis). That is, each element of a sequence corresponds to a two-dimensional characteristic, respectively, a position in time and an assigned value of a defined medium of exchange, typically a monetary value. Accordingly, the x-axis of the mapping depicts trading interval Δ N    315  for a defined trading event. Trading interval Δ N    315  is described by offer interval sequence δ, specifically by constituent offer intervals δ 1 , δ 2 , . . . , δ N . Although trading interval Δ N , may be predefined, it also may be determinable by a seller. Of course, a buyer may terminate involvement in a trade by discontinuing involvement in the trade. Trade will continue if other buyers are participating in the trade, and sufficient inventory is available. Similarly, the y-axis of the process mapping depicts the range of offer value sequence ρ, including constituent offer values, ρ 1 , ρ 2 , . . . , ρ N . Each randomized offer value ρ i  respectively and uniquely corresponds to an offer interval δ i  having the same i th  index value (where i=1 to N).  
      Trading interval Δ N    315  begins at t 0    305  and may run until t N    310  such that the maximum time allocated for trading interval Δ N    315  is symbolized by:
 
Δ N   =t   N   −t   0 
 
 As discussed with respect to  FIG. 1 , above, the maximum time allocated for trading interval Δ N    315  also may be expressed as the sum of the constituent offer intervals δ 1 , δ 2 , . . . , δ N . That is:  
         Δ   N     =       ∑     i   =   1     N     ⁢           ⁢     ∂   i           
 
 Trading event interval Δ N  makes reference to a “maximum” time although, in practice, a predefined trading event may terminate before this maximum time span is reached. A trading event also may be extended, at the discretion of the seller. With the predefined trading event beginning at t 0    305 , the first offer interval δ 1 ,  320  is defined to span interval t 0  to t 1 , second offer interval δ 2    325  is defined to span interval t 1  to t 2 , and so on, up to N th  offer interval δ N    330 , which is defined to span interval t N−1  to t N . In  FIG. 3 , offer intervals δ i  are illustrated to be deterministic in time domain. In this example, offer intervals δ i  generally are of the same duration. As will be seen with respect to  FIG. 4  and  FIG. 5 , the duration of offer intervals δ i  also may be stochastic. Therefore, both deterministic and non-deterministic domain values, e.g., offer intervals δ i , are within the scope of the present invention. 
 
      Turning now to the description of range dimension ρ, a sequence of stochastic offer values ρ i  can be generated by a preselected non-deterministic process, such as one of many, well-known pseudo-random number generators (PRNG), so that the sequence generally does not exhibit a determinable pattern over time. Advantageously, offer values ρ i  may be defined to vary between a preselected floor value └α┘  330  and a preselected ceiling value ┌ω┐  335 . Furthermore, offer values ρ i  can be generated to lie within a preselected distribution envelope, with a mean value μ  340 . In the context of  FIG. 2 , seller  205  may generate the &lt;δ,ρ&gt; dimensions of stochastic decision tuple  225 , using preselected non-deterministic process  300 , either prior to, or during (“on-the-fly”), a trading event. In certain embodiments, preselected floor value └α┘  330  can correspond to the lowest offer values ρ i  that a seller is willing to accept for a particular trade object, during a particular trading event. For example, preselected floor value └α┘  330  may reflect a seller&#39;s cost-to-market price for the preselected trade object subject to the trading event. Similarly, preselected ceiling value ┌ω┐  335  can correspond to the highest offer value ρ i  that a buyer may be willing to pay for a particular trade object, during a particular trading event. Again, by example, preselected ceiling value ┌ω┐  335  may reflect an identified maximum market value (e.g., manufacturer&#39;s suggested retail price) for the preselected trade object subject to the trading event. In addition, mean value μ  340  can correspond to the target price that seller  205  assigns to the preselected trade object. This target price may reflect an acceptable gain or margin that the seller may expect to extract, on average, from the buyers as a result of trading event transactions. Although preselected ceiling value ┌ω┐  335 , preselected floor value └α┘  330 , and mean value μ  340  may generally characterize the expected outcomes from process  300 , it may be beneficial to shape, or weight, the distribution of offer values ρ i , such that the variance of offer values ρ i  may increase, decrease, or be shifted to a range closer to preselected ceiling value ┌ω┐  335 , or preselected floor value └α┘  330 . As a result, the initial mean value μ  340  expectation may be varied, as well, for example, to reflect market conditions and to modify a present buyer response.  
      Process  300  is disposed to generate a particular offer value ρ for a corresponding interval δ. Broadly stated, two significant components of stochastic process generation include a pseudo-random number generation (PRNG) technique and the selected probability distribution function  (x). In general, the PRNG device or technique generates randomized values corresponding to a dimension; the selected probability distribution function  (x) can be used to shape the distribution envelope of the PRNG output. The dimension can be randomized PRNG outcomes that are assigned as offer values ρ. A distribution envelope corresponding to  (x) describes general bounds of the sample space within which a sequence of offer values ρ are generated, as well as the spatial position within the dimension, or value assigned to one sample relative to another. It is desirable to use a PRNG device or technique that does not exhibit an undesired value bias; does not demonstrate a unique, short-term “signature” sequence; or is not susceptible to identification through prolonged observations. These are well known in the sciences, engineering, and applied mathematics arts, and will not be elaborated. By carefully selecting a probability distribution function  (x) to cooperate with a PRNG, the randomized values produced can be substantially within a definable subspace of possible PRNG outcomes. Moreover, the definable subspace of  (x) outcomes can be shaped so that the values resulting from the outcomes can be generally distributed within a preselected distribution envelope. For example, preselected stochastic process  300  may generate random portions of a dimension according to a normal, or Gaussian, probability distribution, which tends to produce random portions in a range described by the familiar “bell curve”-shaped distribution envelope, relative to a preselected mean value μ  340 . Where preselected stochastic process  300  employs a uniform probability distribution to produce a randomized portion of a dimension, the random portion tends to be distributed within a rectilinear, e.g., generally square or rectangular, distribution envelope, relative to the preselected mean value μ  340 . Similarly, preselected stochastic process  300  can be selectively adapted with a myriad of other probability distributions, well-known by ordinary practitioners. These distributions can be weighted, skewed, multimodal, or composites of other probability distributions. Non-limiting examples of probability distributions that may be used include, alone or in combination, Cauchy, Cosine, Double Gamma, Laplace, and Student&#39;s-t distributions, as well as Beta, Burr, Chi, Fisk, Log Normal, and Triangular distributions. A distribution envelope may be approximated by preselected ceiling value ┌ω┐  335  and preselected floor value └α┘  330 , respectively. However, it may be advantageous to approximate upper and lower boundary regions by range values that may be approximated by functions other than by preselected ceiling value ┌ω┐  335  and preselected floor value └α┘  330 , respectively. In addition to receiving the above treatment, an offer value ρ, or sequence of offer values ρ i , may be scaled, normalized, or be otherwise dimensionally adapted to the desired range of offer values ρ i . As used herein, one or both of floor value └α┘  330  and ceiling value ┌ω┐  335  also may have a flexible magnitude responsive to an adaptive process.  
      Returning to  FIG. 3 , first stochastic decision tuple &lt;δ 1 ,ρ 1 &gt; is an initial transaction query that signals the beginning of trade interval Δ N    315  at t 0    305 . First stochastic decision tuple &lt;δ 1 ,ρ 1 &gt; generally indicates that, for the duration of first offer interval δ 1    320 , i.e., from t 0  to t 1 , a preselected trade object made be traded (e.g., purchased) for the amount described by first trade value ρ i    345 . However, the offer at first value ρ 1    345  is time-limited—unless the buyer signals a commitment to trade at trade value ρ 1    345  before the expiration of trading interval δ 1    320 , the offer will be revoked at t 1 . At t 1 , the dimensions associated with second stochastic decision tuple &lt;δ 2 ,ρ 2 &gt;are in force. That is, for the duration of second offer interval δ 2 , i.e., from t 1  to t 2 , the preselected trade object made be traded for the amount described by second trade value ρ 2    350 . As with first trade value ρ 1    345 , the offer to trade at second offer value ρ 2    350  is limited to the duration of second offer interval δ 2 . Provided the trading event is not terminated, an unanswered seller query with stochastic decision tuple &lt;δ k ,ρ k &gt; evokes a subsequent query with stochastic decision tuple &lt;δ k+1 ,ρ k+1 &gt;, with repeated querying continuing until the values of the last stochastic decision tuple &lt;δ N ,ρ N &gt;become effective at t N−1 . The duration of final offer interval δ N    330  begins at about t N−1  and continues until t N    310 , at which time, event interval Δ N    315  expires, typically bringing the corresponding trading event to an end. During final offer interval δ N    330 , final offer value ρ N    355  is considered to be valid. Upon completion of the N th  offer interval of event interval Δ N    315 , final offer value ρ N    355  also is revoked, any unconcealed, committed transactions can be cleared. If necessary, logistics and financial arrangements can be made for finalizing the transaction at the agreed offer value ρ k  and for transferring the selected trade object to the buyer.  
      Selected embodiments also provide seller  205  with the ability to interject promotional offer value pp for the duration of a selected offer interval, here, offer interval δ 8 . As with other offer values, it may be advantageous to prepare promotional token &lt;δ k ,ρ P &gt;in advance of the k th  period in which it will be used, for example, prior to the trading event commences(i.e., before t 0 ), or on-the-fly, during the trading event. Promotional offer value ρ p  may be a desirable inducement for potential new buyers to join the selected trading event, or for participating buyers to gain a heightened sense of excitement and entertainment while awaiting from seller  205 , a potential transaction query having promotional token &lt;δ k ,ρ p &gt;. Promotional token &lt;δ k ,ρ p &gt;may be provided with a shorter offer interval δ k  than is provided otherwise. Typically, desirable response behaviors, which are induced in buyer  210  by promotional token &lt;δ k ,ρ p &gt;may include intended desirable perturbations, including surprise and excitement; more pragmatically, induced behaviors further may include motivating buyer  210  to commit to the transaction proposed by ρ p , as well as a sense of urgency, for example, to decide whether to COMMIT to the promotional offer, and to do so before promotional offer interval δ k  expires. In a commercial implementation, promotional offer value ρ p  may be, for example, an offer value substantially below seller cost; a premium or promotional benefit such as free merchandise, services, and the like; and a combination thereof. In other implementations, promotional offer value ρ p  may represent a limited opportunity to obtain enhanced priority, services, or both; as well as a large perturbation, intended to motivate the perturbed party to respond in an intended manner, desired by the party signaling the perturbation.  
      In certain selected embodiments, more than one promotional offer value ρ p  may be provided, seriatim. In certain other selected embodiments, promotional offer value ρ p , can be derived using a preselected Transaction Driver function Z that influences offer value ρ p  according to a predefined dimensional relationship. The predefined dimensional relationship generally is a function of one or more trade dimensions. The predefined dimensional relationship may be multifactored, with the constituent dimensional factors be combined linearly, non-linearly, or a combination thereof. For example, Transaction Driver function Z can be defined in terms of trade-dimension-related values, such as trade period interval δ t , trade inventory interval, δ q , trade object cost difference, δ c , trade margin value δ m , or, at least one trade indicator or trade dimension, or more if in combination, as may be generally represented by Operational function δ x . Trade object price ρ i  can be influenced or determined by Transaction Driver function Z, for example:
 
ρ f ∝ρ p +∂ m (∂ x −Z)
 
      That is, the trade price ρ f  at which a trade object is offered for sale is generally proportional to a promotional price ρ p  as modified by the influence of Transaction Driver function Z, for example, on a margin variable δ m . In selected embodiments, Transaction Driver function Z can be a thresholding function, which can appear as an unexpected price drop, thereby inducing the desired consumer behavior.  
       FIG. 4  also is a mapping representative of possible outcomes of stochastic dimensioning process (generally at  400 ), which may be used to generate stochastic decision tuple sequence &lt;δ,ρ&gt;. For clarity, the mapping of process  400  is two-dimensional, within the time domain (x-axis) and a “price” range (y-axis). That is, each element of a sequence corresponds to a two-dimensional characteristic, respectively, a position in time and an assigned value of a defined medium of exchange, typically a monetary value. Accordingly, the x-axis of the mapping depicts trading interval Δ N    415  for a defined trading event. Trading interval Δ N    415  is described by offer interval sequence δ, specifically by constituent offer intervals δ 1 , δ 2 , . . . , δ N . Similarly, the y-axis of the process mapping depicts the range of offer value sequence ρ, including constituent offer values, ρ 1 , ρ 2 , . . . , ρ N . Similar to  FIG. 3 , offer values ρ i  can vary randomly in nature. By carefully selecting a probability distribution function  (x) to shape the randomized range of values output by a PRNG, a definable subspace of possible PRNG outcomes generally may be approximated by a preselected distribution envelope described by probability distribution function  (x).  
      Unlike  FIG. 3 , in which offer intervals δ i  are depicted as having a generally uniform duration, offer intervals δ i  of  FIG. 4  are stochastic in nature. That is, the duration of selected offer intervals δ i  may vary substantially randomly. Conveniently, probability distribution function  (x) may be used to generate both offer values ρ i  and offer intervals δ i . However, the domain of values over which offer intervals δ i  run may be generated instead by probability distribution function  (x), where ( (x) ≠  (x)). Desirably, each randomized offer value ρ i  can respectively, and may uniquely, correspond to an offer interval δ i  having the same i th  index value (where i=1 to N).  
      A trading event, within the context of process  400 , may transpire over trading interval Δ N    402 , which may run from t 0    405  to t N    407 . Although trading interval Δ N , may be predefined, it also may be determinable by a seller. Of course, a buyer may terminate involvement in a trade by discontinuing involvement in the trade. Trade will continue if other buyers are participating in the trade, and sufficient inventory is available. First offer interval δ 1    403  may run between t 0    405  and t 1 , corresponding to first offer value ρ 1    430 . Second offer interval δ 2    404  may run between t 1    405  and t 2 , corresponding to second offer value ρ 2    440 . Offer intervals may be further divided logically, such that final offer period δ N    495 , may run between about t N−1  and t N    407 , and may correspond to final offer value ρ N    455 . A trading event also may be terminated before the entire trading interval  402  elapses, or may be extended, for example, at the discretion of seller  205 . Because of their stochastic nature, selected ones of offer intervals δ 1 , δ 2 , . . . , δ N  may have durations longer than, shorter than, or of approximately the same duration as, selected other offer intervals δ 1 , δ 2 , . . . , δ N . The selected duration of an offer interval δ i , can be generated by probability distribution function  (x) to vary generally between predetermined minimum offer interval δ L    485  and predetermined maximum offer interval δ u    490 . Probability distribution function  (x) can be selected such that the corresponding distribution envelope of the offer interval δ i  substantially conforms to the sample subspace desired.  
      In selected embodiments of the present invention, one or more offer intervals δ 1 , δ 2 , . . . , δ N  occurring during trading interval Δ N    402 , may not be stochastic in nature, but be deterministic, for example, defined by a dimension other than time, such as allocated inventory. In the example of allocated inventory, a deterministic interval offer interval δ f  terminates upon exhaustion of the allocated inventory or, more generally, upon a condition established by other, non-temporal dimensions. The entire temporal component of trading interval Δ N    402  may be considered to be generally non-deterministic, even if a deterministic offer interval δ f  is interposed therein. Similarly, offer value ρ p , also may be, at least in part, deterministic, and also may be established to correspond to a trading dimension, including, without limitation, existing or allocated inventory, product type, and so forth.  
      Similar to stochastic process  300  in  FIG. 3 , two-dimensional non-deterministic process  400  in  FIG. 4  can implement one or more well-known PRNG devices and techniques (PRNG), in one or more dimensions, to generate sequences of stochastic offer values ρ i  and stochastic offer intervals δ i . Corresponding respective probability distribution functions,  (x) and  (x), may be preselected to cooperate with the. PRNG so that the randomized values produced thereby can be substantially within a definable subspace of possible PRNG outcomes. Also, preselected stochastic process  400  can be chosen from among one or more of a wide array of weighted, skewed, multimodal, or composite, probability distributions, with each distribution typically being dispersed around a preselected mean value. In  FIG. 3 , stochastic offer values ρ i  may vary between a preselected floor value └α┘  330  and a preselected ceiling value ┌ω┐  335 , within a preselected distribution envelope dispersed about mean value μ  340 . Likewise, the stochastic offer values ρ i  in  FIG. 4  may vary between a preselected floor value └α┘  415  and a preselected ceiling value ┌ω┐  425 , within a preselected distribution envelope dispersed about mean offer value μ  445 . Offer intervals δ i  may vary between predetermined minimum offer interval δ L    485  and predetermined maximum offer interval δ u    490 , within a preselected distribution envelope, which may be distributed about some mean interval value (not shown). Non-limiting examples of probability distributions that may be used include, alone or in combination, Uniform, Gaussian, Cauchy, Cosine, Double Gamma, Laplace, and Student&#39;s-t distributions, as well as Beta, Burr, Chi, Fisk, Log Normal, and Triangular continuous distributions, as well the gamut of suitably chosen discrete distributions.  
      Unlike process  300  in  FIG. 3 , embodiments according to process  400  in  FIG. 4  may possess an adapted mean value μ  445 , which may result from implementation of adapted upper target offer value ξ  430  and adapted lower target offer value β  420 . It may be desirable to adapt one or both of value ξ  430  and value β  420  in response to factors of the environment in which the trading event occurs. Where transactions described herein are within a commercial context, environment factors can include trade object supply side environment factors (e.g., availability of trade objects from a supplier), trade object demand side environment factors (e.g., demand trends among consumers), as well as other environment factors including, without limitation, fluctuations in overhead expenses; changes in finance, energy and transport costs; geopolitical factors; and so on). The adapted trade range between upper value ξ  430  and lower value β  420  also may be indicative of a range of offer values ρ i , which has been determined, such as by seller  205  in  FIG. 2 , to be representative of a range in which buyer  210  is more likely to COMMIT to a transaction. In general, an increase in one or a paired increase in both of adapted lower target offer value β  420  and adapted upper target offer value ξ  430 , may result in an increase in mean value μ  445 .  
      Should preselected floor value └α┘  415  generally correspond to, for example, the cost-to-market to seller  205  for a trade object, the effect of raising selected lower target offer value β  420  can be to increase the margin of seller  205 . By contrast, a decrease in one or a paired decrease by both of adapted lower target offer value β  420  and adapted upper target offer value ξ  430 , may result in a decrease in adapted mean value μ  445 . This reflects a tendency for a transaction to bring a lower offer value ρ i  for a given trade object. Should preselected floor value └α┘  415  be representative of the cost-to-market to seller  205  for a trade object, the aforementioned tendency to decrease adapted mean value μ  445  generally reflects a tendency for buyer  210  to make a transaction for a trade object at a savings and a tendency for seller  205  to yield a lower margin from the transaction.  
      Of course, a trend towards a lower price for a trade object, typically results in a trend for additional transactions for the object, which may be desirable for seller  205 . Advantageously, adapted lower target offer value β  420  and adapted upper target offer value ξ  430  can cooperate such that stochastic offer values ρ i  may vary between adapted lower target offer value β  420  and adapted upper target offer value ξ  430 , within a preselected distribution envelope dispersed about adapted mean value μ  445 . Importantly, adapted lower target offer value β  420  and adapted upper target offer value ξ  430  may be so adapted before, during, or after a trading event. For an example during a trading event, if seller  205  notices a reluctance to transact on the part of buyer  210 , seller  205  may reduce one or both of adapted lower target offer value β  420  and adapted upper target offer value ξ  430  to result in a decreasing trend in adapted mean value μ  445 . Thus, although buyer  210  may still perceive one or both of offer intervals δ i  and offer values ρ i  as being generally stochastic, the distribution envelope characterizing offer values ρ i  may be perceived as tending lower, thereby tending to induce buyer  210  to COMMIT to make a transaction. Not only may adapted lower target offer value β  420  and adapted upper target offer value ξ  430  be adapted dynamically (on-the-fly), for example, to shift adapted mean value μ  445  higher or lower, the distribution envelope corresponding to the values produced for process  400  also may be adapted.  
      For example, it may be desirable to reduce (or increase) adapted mean value μ  445 , as well as to adapt distribution function  (x) such that offer values ρ i  are generated within an exemplary Gaussian distribution envelope instead of an exemplary Uniform distribution. Therefore, embodiments of the present invention provide methods and apparatus offering flexibility in generation of the stochastic characteristics of a trade object, as perceived by an engaged transactor. Flexibility in the dimension of offer values ρ i  can be complemented by flexibility in the dimension of offer intervals δ i . That is, embodiments of the present invention provide methods and apparatus offering flexibility in generation of the stochastic characteristics of a trade event, as perceived by an engaged transactor. For example, it may be desirable to reduce (or increase) a mean value for offer interval δ i , as well as to adapt distribution function  (x) such that offer intervals δ i  are generated within an exemplary Gaussian distribution envelope instead of an exemplary Uniform distribution. Distribution function  (x) may be adapted further such that offer intervals δ i  can at least weakly correspond to offer values ρ i . For example, it may be desirable to generate a distribution envelope for offer intervals δ i  such that offer intervals δ i  tend to be shorter when offer values ρ i  approach the extrema of the distribution envelope representative of distribution function  (x), and that offer intervals δ i  are generally longer for offer values ρ i  tending toward the mean value μ  445 , representative of function  (x). However, another result, and another correspondence, between offer intervals δ i  and offer values ρ i  may be desired. Nevertheless, according to the teaching herein, methods and apparatus so adapted readily may achieved a desired result and a target correspondence.  
       FIG. 5  is yet another mapping, representative of possible outcomes of plural stochastic dimension process ensemble (generally at  500 ), which may be used to generate stochastic decision tuple sequences &lt;δ,ρ&gt;. However, unlike  FIG. 4 , in which each dimension (δ i ,ρ i ) can be drawn from one process, sequences representative of each dimension (δ i ,ρ i ) may be generated using multiple, disparate stochastic processes and drawn from multiple, disparate, distribution envelopes, yet be adaptably and controllably generated within a desired space. Stochastic process  500  may be constructed from plural subprocesses, in a building-block fashion. Such a composite process can generate controllable, deterministic outcomes that can be used to form one or more stochastic dimension sequences. The selected subprocesses of the composite stochastic process also may be stochastic in nature, and adapted to yield selected dimension portions, which generally may lie within a definable subspace. As with previously recited stochastic values, the values generated by process  500 , are adapted to induce a desired behavior in a selected perceiver, such as, for example, second transactor  120 , in  FIG. 1 , or buyer  210  in  FIG. 2 . The adapted values generated by process  500  may include one or both of stochastic offer value ρ i  and stochastic offer interval δ i .  
      Stochastic offer intervals δ i  may vary between adapted minimum offer interval δ L    585  and adapted maximum offer interval δ u    590 , within a preselected distribution envelope, and which may be distributed about some mean interval value (not shown). Likewise, stochastic offer values ρ i  may vary between a preselected floor value └α┘  515  and a preselected ceiling value ┌ω┐  525 , dispersed about adapted mean offer value μ  545 , within a preselected distribution envelope. Adapted mean value μ  545  may result from implementation of adapted upper target offer value ξ  530  and adapted lower target offer value β  520 , positioned between ┌ω┐  525  and └α┘  515 . Similar to value ξ  430  and value β  420  in  FIG. 4 , it may be desirable to adapt one or both of value ξ  530  and value β  520 , in response to factors of the environment in which the trading event occurs. Importantly, adapted lower target offer value β  520  and adapted upper target offer value ξ  530  may be so adapted before, during, or after a trading event.  
      Unlike the process  300  in  FIG. 3 , or process  400  in  FIG. 4 , stochastic process  500  in  FIG. 5  is a composite process, which represents an ensemble, or defined group, of random processes ξ 1 , ξ 2 , . . . , ξ M . One or more sequence values &lt;δ i ,ρ i &gt;.may be generated by one or more of the ensemble of random processes ξ 1 , ξ 2 , . . . , ξ M . Ensemble members ξ 1 , ξ 2 , . . . , ξ M can be used to generate sequence values in numerous ways. In one exemplary technique, each &lt;δ i ,ρ i &gt; stochastic decision tuple may be generated by corresponding process ξ i , which itself may include suitable PRNG to generate values of &lt;δ i ,ρ i &gt; using functions  (x) and  (x), respectively. In another exemplary technique, each &lt;δ i ,ρ i &gt; stochastic decision tuple may be generated by a randomly-selected ensemble member ξ i , as is illustrated in  FIG. 5 . In certain embodiments, one ensemble member ξ may be provided for each offer interval δ i  in trading interval  502 . In others, there may be fewer ensemble members ξ than offer intervals δ i . In such a case, it is desirable to re-use ensemble member functions ξ, so that member functions ξ may be used multiple times to generate offer interval δ i  together with offer value ρ i . In certain embodiments, it is advantageous to generate stochastic decision tuple &lt;δ i ,ρ i &gt;.in real-time, or near-real-time, as a trading event transpires. In other embodiments, it may be advantageous to generate stochastic decision tuple &lt;δ i ,ρ i &gt; prior to the trading event. As indicated above, by applying a selected distribution function to outcomes generated by a PRNG, the boundaries and shape of the process subspace can be controlled using, for example, mean value, boundary values, and adapted target values as input for the processes of ξ. Such piecewise control of the stochastic process represented by process  500 , stochastic decision tuple &lt;δ i ,ρ i &gt; values can be shaped and clustered to adapt to, and to at least weakly correspond with, an external process, which may be transpiring at least partially concurrently with process  500 . Such an external process could include, for example, music, live or recorded events, and the like. Thus, according to the teachings herein, stochastic process  500  could provide stochastic decision tuple &lt;δ i ,ρ i &gt; in a manner that allows selected values of &lt;δ i ,ρ i &gt; remain at least stochastic and randomized, yet appear as if they bear some coordination with the external process. As before, non-limiting examples of probability distributions that may be used include, alone or in combination, Uniform, Gaussian, Cauchy, Cosine, Double Gamma, Laplace, and Student&#39;s-t distributions, as well as Beta, Burr, Chi, Fisk, Log Normal, and Triangular continuous distributions, as well the gamut of suitably chosen discrete distributions.  
      Further to  FIG. 5 , trading interval  502  can begin at t 0    505  with onset of first offer interval δ 1    503  and continue until t 1 , at which time second offer interval δ 2    504 , begins. Prior to t 0 , ensemble member process ξ 5  generates first stochastic decision tuple &lt;δ 1 ,ρ 1 &gt; which can be signaled to a selected perceiver, such as second transactor  102  in  FIG. 1  or buyer  210  in  FIG. 2 . Generally following the signaling protocol described, for example, with respect to  FIG. 2 , buyer  210  perceives offer value ρ 1  and, if desirous to make a transaction with seller  205 , buyer  210  signals a COMMIT response to seller  205  before offer interval  67   1  expires. Prior to the expiration of first offer interval δ 1 , ensemble member process ξ 3  generates second stochastic decision tuple &lt;δ 2 ,ρ 2 &gt;. Should buyer  210  not respond before the end of first offer interval δ 1 , or does not otherwise provide a COMMIT response, second stochastic decision tuple &lt;δ 2 ,ρ 2 &gt; can be signaled to buyer  210  before first offer interval δ 1  expires. At t 1 , the trade object, which is available for trading, can be offered by seller  205  to buyer  210  for second offer value ρ 2 , with this value being valid for only a period of δ 2  interval  504 . Prior to the end of second offer interval δ 2 , ensemble member process ξ 8  can generate third stochastic decision tuple &lt;δ 3 ,ρ 3 &gt;, which is signaled to buyer  210  before t 2 . In general, the generation of new stochastic decision tuples &lt;δ 1 ,ρ 1 &gt; may repeat throughout trading interval  502 , with ensemble member process ξ 4  generating N th  decision tuple &lt;δ N ,ρ N &gt; for use with N th  offer interval δ N    595 , typically terminating at t N    507 . Similar to process  400  in  FIG. 4 , offer intervals may vary substantially randomly between adapted lower bound offer interval δ L    585 , and adapted upper bound offer interval δ u    590 . In addition, a promotional decision tuple &lt;δ P ,ρ P &gt; can be signaled to buyer  210  in advance of promotional offer interval δ p . Promotional decision tuple &lt;δ P ,ρ P &gt; may be interjected by seller  205  during the transpiration of event interval  502 , or may be interjected in advance, for example, during an advanced generation of decision tuples &lt;δ,ρ&gt; while planning for a particular trading event. Offer intervals δ i  and offer values ρ p , may selectively be generated and presented, using composite stochastic methods herein, and used within the context of an entertainment schema. For example, in an milieu, the signaling of stochastic decision tuples &lt;δ,ρ&gt; can be coordinated with audio and visual indicia, including music, sounds, dramatic images, and the like, to heighten excitement and interest in a particular trading event. Buyer  210  may be induced into behaving in a desired way, for example, committing to making a trade, for a trade object offered during a trade interval, in response to perceiving the stochastic decision tuples &lt;δ,ρ&gt;. Process  500  may be one of many such transaction processes, which may be proceeding, whether simultaneously or serially, in which it may be desirable for seller  205  to monitor and adjust, as desired, adapted upper target offer value ξ  530  and adapted lower target offer value β  520 , which may be common to at least some of these transaction processes In this manner, seller  205  is provided with methods and apparatus to adapt the trading event milieu, such as trade object pricing and trading event pacing, to a desired range. Seller  205  also can be enabled to adapt and adjust profit margin, clearance prices, promotional events, and so on, and to differentiate trade object transactions for selected classes of buyers  210 .  
       FIGS. 6, 7 , and  8  are exemplary embodiments of adaptive stochastic transaction systems, respectively corresponding to the  FIG. 3 ,  FIG. 4 , and  FIG. 5 .  
       FIG. 6  symbolically depicts exemplary stochastic sequence generator  602 , as an element of adaptive stochastic transaction system  600 . Stochastic sequence generator  602  can be representative of one possible embodiment by which stochastic decision tuple &lt;δ t ,ρ i &gt;  605  may be formed. Broadly, stochastic decision tuple &lt;δ t ,ρ i &gt;  605  may be signaled, as variable element of stochastic transaction process  610 , by way of communication channel  685  to transactor C 1    690 . Desirably, when perceived, stochastic decision tuple &lt;δ t ,ρ i &gt;  605  is adapted to induce a desired behavior in transactor C 1    690 . Advantageously, system  600  may use behaviors of one or more transactor C 1    690 , as feedback signal  695 , to adapt system  600  (e.g., through output communication path  685 ) to a behavior of transactor C 1    690 .  
       FIG. 7  symbolically depicts adaptive stochastic transaction system  700 , as employing one possible embodiment stochastic sequence generator  702  by which the stochastic sequence of process  400  in  FIG. 4  may be generated. Stochastic sequence generator  702  can accept variable inputs  725 ,  726 ,  770 ,  772  from enterprise module  704  to produce stochastic decision tuple  705 . Within enterprise module  704 , upper and lower bounds for offer values ρ j  can be shaped by ceiling value  715  and floor value  717 , respectively. Similarly, offer interval δ j  can be bounded by maximum offer interval length  720  and minimum offer interval length  722 . Each of value bounds  715 ,  717  and interval bounds  720 ,  722  may be responsive to enterprise operations feedback from operations executive module  706 . Module  706  may monitor operational parameters via command and intelligence links  718 ,  795 . Such operational parameters may include data being transmitted to one or more of transactors C 1    790   a  to C N    790   n  via communication network  777 ; remote transactional information and control data  795 , for example the number of transactors  790   a ,  790   n  currently coupled to module  702 , the nature and magnitude of the transactions being executed; remote transactor  790   a ,  790   n  control responses and geolocations; and channel conditions in network  777 , including available bandwidth, throughput, quality of service, latency, and return trip time of probe packets.  
      Stochastic process generator  750  may produce offer values ρ j    760  in response to desired upper and lower offer value guidelines  730 ,  735  within which offer value ρ j    760  can be predominantly distributed. In certain implementations of the present invention, pseudorandom number generator  740  can produce a pseudorandom variable representative of offer value ρ j    760  generally within the range represented by value guidelines  730 ,  735 . Stochastic process conditioner  745  may be employed to adjust offer value ρ j    760  to generally conform to a predetermined process envelope and stochastic distribution, which may be approximately centered about desired mean offer value μ, responsive to distribution shaping function f x . Similarly, stochastic process generator  752  may produce offer interval δ j    765  generally within the range represented by interval guidelines  732 ,  736 , as may be limited by interval bounds  720 ,  722 . Pseudorandom number generator  742  can be employed to produce a pseudorandom value generally within the range represented by guidelines  732 ,  736 . As with offer value ρ j    760 , it may be desirable to provide multiple offer intervals δ j    765  that generally conform to a predetermined process envelope and stochastic distribution, responsive to distribution shaping function f y . Tuple generator  780  associates offer value ρ j    760  offer intervals δ j    765  for a given index j, producing decision tuple &lt;ρ j , δ j &gt;  705 . Each tuple thus produced can be assembled within stochastic ensemble generator  708 , to produce a selected sequence of decision tuples &lt;ρ j ,δ j &gt;  705 , associated with the trade object offered during the particular trading event at hand. Ensemble generator  708  can be enabled to transmit via enterprise communications module  710  to remote transactors  790   a ,  790   n.    
       FIG. 8  symbolically depicts adaptive stochastic transaction system  800 , as employing one possible embodiment stochastic sequence generator  802  by which the stochastic sequence of process  500  in  FIG. 5  may be generated. Stochastic sequence generator  802  can accept variable inputs  825 ,  826 ,  870 ,  872  from enterprise module  704  to produce stochastic decision tuple  805 . Within enterprise module  804 , upper and lower bounds for offer values ρ j  can be shaped by ceiling value  715  and floor value  817 , respectively. Similarly, offer interval δ j  can be bounded by maximum offer interval length  820  and minimum offer interval length  822 . Each of value bounds  815 ,  817  and interval bounds  820 ,  822  may be responsive to enterprise operations feedback from operations executive module  806 . Module  806  may monitor operational parameters via command and intelligence links  818 ,  895 . Such operational parameters may include data being transmitted to one or more of transactors C 1    890   a  to C N    890   n  via communication network  777 ; remote transactional information and control data  895 , for example the number of transactors  890   a ,  890   n  currently coupled to module  802 , the nature and magnitude of the transactions being executed; remote transactor  890   a ,  890   n  control responses and geolocations; and channel conditions in network  777 , including available bandwidth, throughput, quality of service, latency, and return trip time of probe packets.  
      Stochastic process generator  850  may produce offer values ρ j    860  in response to desired upper and lower offer value guidelines  830 ,  835  within which offer value ρ j    860  can be predominantly distributed. In certain implementations of the present invention, pseudorandom number generator  840  can produce a pseudorandom variable representative of offer value ρ j    860  generally within the range represented by value guidelines  830 ,  835 . Stochastic process conditioner  845  may be employed to adjust offer value ρ j    860  to generally conform to a predetermined process envelope and stochastic distribution, which may be approximately centered about desired mean offer value μ, responsive to distribution shaping function f x . Similarly, stochastic process generator  852  may produce offer interval δ j    865  generally within the range represented by interval guidelines  832 ,  836 , as may be limited by interval bounds  820 ,  822 . Pseudorandom number generator  842  can be employed to produce a pseudorandom value generally within the range represented by guidelines  832 ,  836 . As with offer value ρ j    860 , it may be desirable to provide multiple offer intervals δ j    865  that generally conform to a predetermined process envelope and stochastic distribution, responsive to distribution shaping function f y . Tuple generator  880  associates offer value ρ j    860  offer intervals δ j    865  for a given index j, producing decision tuple &lt;ρ j ,δ j &gt;  805 . Each tuple thus produced can be assembled within stochastic ensemble generator  805 , to produce a selected sequence of decision tuples &lt;ρ j , δ j &gt; corresponding to plural sequence ensembles  808   a - 808   m , each ensemble being associated with the trade object offered during the particular trading event at hand.  
      Tuple sequences associated with respective ensemble  808   a - 808   m  may have respective preselected mean values, distribution function envelope, and other process parameters that differ from others of ensembles  808   a - 808   m . Ensemble generator  805  can select tuples from selected one of respective ensemble  808   a - 808   m  perhaps in response to real-time feedback from remote transactors  890   a ,  890   n ; from profit, loss, inventory, and demographic information provided through module  806 ; or both. Moreover, given the selectability of the length and characteristics of multiple sequences selectable from generator  805 , predictive or anticipatory action to impair the fairness or integrity of system  800  can be minimized, due to the employing multiple processes, generating multiple non-identical ensembles of stochastic decision tuple &lt;δ i ,ρ i &gt;, and intermixing potentially variable sequences of stochastic decision tuple &lt;δ i ,ρ i &gt; drawn from different ensembles and different processes.  
       FIG. 9  depicts an embodiment of a graphical user interface (GUI)  900 , as may be perceived by a user/buyer (not shown), such as transactor T 2    120  in  FIG. 1 , or consumer C  210  in  FIG. 2  (generally, “purchaser”). Interface  900  may be useful to illustrate functions and features of selected methods embodied herein. GUI  900  is representative of computer code executing in a computer system used to display information to the purchaser, in the form of descriptors, which may be considered relevant to the purchaser&#39;s decision to purchase, or agreement to purchase, a selected trade object during a selected trading event. For example, the descriptors of GUI  900  can indicate to the purchaser: that a transaction is in progress; that trade object  902  is featured during the trading event; that trade object  902  may be purchased at current offer value  908 ; that current offer value  908  will remain valid during the offer interval  910 ; that the remaining time for the event  912  represents the remaining period of the trading interval; and that a determinable number of trade objects  914  currently exist in inventory.  
      GUI  900  can be representative of computer code executing in a computer system to provide additional information, which may be useful to the purchaser in evaluating the beneficial aspects of the transaction may include specific inventory descriptors  904 , and a manufacturer&#39;s suggested retail price  906 , which allow the purchaser to make independent appraisals of the actual value and desirability of trade object  902 . Additional descriptors to enhance the personalized trading milieu represented by GUI  900  may include purchaser name or trading identifier  950 , and, if implemented, membership and status descriptors  952 . A seller also may choose to communicate with the purchaser for other purposes, such as offering payment and shipping information to a credit and order fulfillment entity, which may be part of an enterprise including the seller.  
      Excitement and drama can be augmented by providing GUI  900  with perceived experience intensifiers which tend to enhance a prospective buyer&#39;s desire to purchase the trade object. Exemplary perceived experience intensifiers can include any artifice intended to seize the attention of the prospective purchaser including, without limitation, dramatic tones, melodic notes, or other psychoacoustic stimulations; flashing lights, alternating, or chaotic, patterns of colors, or other distinctive imagery apart from visual presentation elements ordinarily on display; tactile feedback; dramatic fluctuations in offer value  908  and intervals  908 ,  910 ; or by any effective combination thereof.  
      In such implementations, it may be advantageous to configure COMMIT selector  925  as a selector that is easy-to-use during trading events. In that regard, selector  925  can be provided as large, colorful icon, which may provide a colorful visual counterpoint to the background of GUI  900 . For example, where selector  925  issues a COMMIT signal by a computer mouse-over-and-click movement, a purchaser may initially position the mouse cursor over selector  925 , wait until the trade descriptors  908 ,  910 ,  912 ,  914  reach a desirable point. At the moment of purchase, the buyer can click a mouse button on selector  925  to COMMIT to purchase the trade object represented by descriptor  902  at the offer value represented by descriptor  908 . In addition, where GUI  900  is representative of computer code executing in a computer system used by the purchaser, which communicates with the seller, the purchaser may be enabled to terminate a COMMIT to a transaction before the end of the trading event indicated by descriptor  912 , by asserting CANCEL selector  930 .  
       FIG. 10  depicts an embodiment of adaptive stochastic transaction system  1000  that includes marketing module  1020 , enterprise module  1025 , and e-commerce module  1035 . Module  1020  may be similar to system  100  in  FIG. 1  and system  200  in  FIG. 2 , although the function and operation of modules  1020 ,  1025 ,  1035  can be viewed as being incorporated into transactor T 1   110  in  FIG. 1  and seller E  205  in  FIG. 2 .  
      In  FIG. 10 , marketing module  1020  is adapted to enable and facilitate trading events between buyer C  1005  and seller E  1010 . A communication route in module  1020  typically includes uplink  1040  and downlink  1030 . In general, once it is communicated from seller E  1010  over downlink  1030  and perceived by buyer C  1005 , a stochastic decision token ψ (not shown) is disposed to induce an observed behavior in buyer C  1005 . Similar to stochastic decision token ψ  160  in  FIG. 1  and stochastic decision tuple &lt;δ,ρ&gt;  225  in  FIG. 2 , et seq., a decision token or tuple transmitted to Buyer C  1005  from seller E  1010  can be representative of at least one of a stochastic offer value and a stochastic offer interval, presently associated with the preselected trade object (not shown), subject to the present transaction. Module  1020  may represent sales and entertainment delivery activities, by which one or more Buyers C  1005 , may engage in transactions with Seller E  1010  in a dynamic and exciting transaction milieu via any form of communication. Buyer C  1005  may be able to interact with seller  1010  using nearly any form of electronic media, whether broadcast, multicast, or unicast, over public computer network or wireless broadcasts, whether by phone, personal electronic communicator, computer, or any contemplated communication device. However, it may be advantageous and efficient to separate sales/trading and entertainment operations from those involved with completing transactions and preparing and promoting new transactions.  
      Accordingly, E-Commerce Module  1035  may include “Back Office” Unit B  1015 , which may provide, without limitation, subscription and pre-approval management, credit and payment processing, order fulfillment, warehousing, shipping, purchasing, accounting, executive and operations management, operations research, broadcasting, networking and systems infrastructure, advertising and marketing, econometrics and market analysis, and ombudsman activities. Back Office Unit B  1015  may interact with consumer C  1005 , a Buyer, for the purpose of accepting and verifying the payment of Buyer C  1005 , for a trade object purchased from Seller E  1010  via Marketing Module  1020 . Unit B  1015  also may receive information from Seller E  1010  such as multi-dimensional data collected during trading operations, one example of which may be Seller E  1010  reporting to executives in Unit B  1015  what prices were paid in a given region for a given trade object at a given time. Indeed, whatever business intelligence may be gleaned by Seller E  1010 , individually, in the aggregate, or both, can be fed back to Unit B  1015 , so that operations of E-Commerce Module  1035 , Enterprise Module  1025 , or both, may be adapted advantageously thereby.  
      In return, within the context of the functions and operations of Enterprise Module  1025 , Unit B  1015  can apprise Seller E  1010  of current and future trading operations, events, and data, such as price floors and ceilings, desired margins, anticipated, available, and allocated inventories of trade objects, and trading times, and locations in which such trading events will be offered. Beneficially, Unit B  1015  can receive information from customers (such as buyer C  1005 ), vendors, lenders, creditors, manufacturers, and competitors, as well as other sources of public and proprietary information to permit long-range, intermediate-term, and short-range decisions as to inventory, prices, channels of commerce and communication, target markets, risk and cost allocation, and any other factor that could be used to determine what objects were offered for trade, where and when they are offered, and at what price.  
      In this regard, embodiments, aspects, and features of marketing module  1020 , enterprise module  1025 , and e-commerce module  1035 , can be devised and coupled to selectively communicate, forming advantageous embodiments of systems and methods for adaptive stochastic transactions. As indicated above, a business operator, such as enterprise module  1025 , may use selected trade indicators to adjust an adaptive stochastic transaction process herein to meet desired business objectives and to influence the behavior of the buyer in real-time, near-real-time, periodically, or episodically.  
      In a case where an undesirable or deleterious trade indicator is measured, a business operator may desire to adapt one aspect of the Transaction Driver function Z to correct or to offset the undesirable indicator. For example, excess prospective buyer activity may be undesirable during a particular trading event, where one objective of the trading event is to increase trade object brand awareness among prospective buyers. Excessive activity in a trading event may quickly deplete the inventory available for the trading event, which, in turn, may terminate the trading event before the trade object receives the desirable amount of viewer exposure. Also, excessive activity can engender in prospective buyers a perception of lesser value of a trade object, and leave in its wake unsatisfied customers. Excessive activity may be indicated by high telephonic call volume or by high network link volume, i.e., too many buyers “just looking.” Erratic responses by groups of prospective buyers also may be representative of an unfavorable trading environment.  
      In such an example, it may be beneficial to adapt the Transaction Driver function Z such that the offered trade object value or price ρ N  trends upward. It is generally recognized that increasing an object&#39;s price can decrease buyer demand. Thus, by allowing the offered trade object value ρ N  to trend upward as can be generated by a stochastically-influenced transaction process, excessive buyer activity can be curtailed. In another example, a business operator may measure a number of network links or telephonic connections that appears disproportionately large compared to the contemporaneous sales volume, and possibly, by other prior measures and trade indicators. This may suggest that a trade object offer value ρ N  is considered by observant prospective buyers as being too high. Responsive to such indicators, a business operator may bias the Transaction Driver function Z to increase, thereby reducing the price ρ N  at which the trade object is offered to prospective buyers. As the price tends to drift stochastically lower, an increase in sales volume may be measured as prospective buyers are induced to transmit a COMMIT token, or functional equivalent thereof, to the seller, and become actual buyers.  
      Also, selected trade indicators may be combined to adapt the Operational function δ x  to a vast variety of trade indicators and measurements of influences both internal to and external to the enterprise. It can be advantageous to selectively combine trade indicators, so that the Operational function δ x  includes a short term weighting factor, intermediate weighting factor, long term weighting factor, or a combination thereof. Short-term weighting factors can be representative of selected trade indicator responding to activities or events of relatively short duration, for instance excess buyer activity during a trading event. An intermediate weighting factor may be derived from a selected trade indicator representative of factors such as fuel costs and energy surcharges which may impact an enterprise through higher operating expenses and trade object purchasing costs over a time longer than short-term factors. A long-term weighting factor may be adapted to reflect strategic goals of the corporation, or regional or demographic factors, and the like.  
      Although the exemplars set forth in the foregoing Figures illustrate temporally-adapting processes and corresponding apparatus, neither the range nor the domain of inventive adaptive stochastic transaction embodiments herein are limited to one particular dimension but, instead, may be defined over plural dimensions, possibly exclusive of the time domain. Applicable dimensions may include aforementioned trade dimensions, such as those influenced by consumer, market, competitor, or enterprise measures.  
      In  FIG. 11 , a trade object inventory level is the trade dimension to which the exemplary adaptive stochastic transaction process  1100  responds. That is, trade object price generally corresponds to trade object inventory. Similarly, trade interval Δ N    1102  is related to trade object inventory, in that trade interval Δ N    1102  can end upon exhaustion of a predefined trade inventory. At the onset of the first interval δ 1 , trade object inventory is measured to be quantity, q 0 . During this interval δ 1 , trade object price can be held at first value ρ 1 . Responsive to measured inventory, for example, Transaction Driver function Z may be used to adjust trade object value ρ. As in the foregoing examples and embodiments, at least one of a trading interval δ i  and a trade object price ρ i , constitute a stochastic decision tuple &lt;δ,ρ&gt;, with which a Buyer may decide to purchase the offered trade object at the trade object price then represented by trade object price ρ i .  
      In certain embodiments using Transaction Driver function Z, measured dimensions constituting Transaction Driver function Z may signal a special trading event in which trade object price will be driven down until trade inventory reaches the preselected minimum quantity, q N . At the end of interval Δ N , which includes the aforementioned special trading event, the corresponding trade object price can be ρ N . Thus, when trade object inventory reaches quantity q N , prospective buyers who transmit a COMMIT token, indicating a desire to buy the trade object during the special trading interval, may purchase trade objects at the final trade object price ρ N , even if a prospective buyer transmitted a COMMIT token corresponding to a trade object purchase price greater than ρ N . However, prospective purchasers who do not transmit a COMMIT token prior to the completion of special trading interval, as marked by trade object inventory reaching the quantity q N , can be precluded from purchasing the trade object at final trade object price ρ N .  
      In selected embodiments, trade object price ρ i  ε {ρ 1 , . . . , ρ N } may fluctuate stochastically for at least a portion of trading event Δ N    1102 , evoking the principles set forth above. In  FIG. 11 , trading event Δ N    1102 , is not defined over time, but over a preselected quantity of trade object inventory. Thus, where q 0    1105  corresponds to an exemplary initial inventory quantity, and q N    1107  corresponds to an exemplary target, or final, inventory quantity, trading event Δ N    1102  can correspond to a preselected inventory reduction quantity. That is, Δ N  {circumflex over (=)}q 0 −q N . In such a case, each trading interval δ i  ε {δ 1 , . . . , δ N } can correspond to an incremental inventory change, e.g., δ N {circumflex over (=)}q N−1  −q N . Also, successive trading intervals δ i  can correspond to fixed and equal incremental inventory changes, or to one or more incremental inventory change that varies deterministically or, at least in part, stochastically. By extension, although trading event Δ N    1102  is illustrated to be generally fixed or strictly defined, embodiments of the present invention also contemplate an extensible trading event Δ N    1102 , in which target, or final, inventory quantity q N    1107 , is changed, e.g., lowered, to permit additional buyers to commit to purchasing the offered trade object.  
      In this example, a stochastic sequence generator (not shown but may be similar to stochastic sequence generator  602  in  FIG. 6 , stochastic sequence generator  702  in  FIG. 7 , or stochastic sequence generator  802  in  FIG. 8 ), may be used to generate a signal value for Transaction Driver function Z from one or more selected trade indicators constituent of Transaction Driver function Z. Where constituent trade indicators of Transaction Driver function Z combine to approximate the Operational function δ x , Transaction Driver function Z can drive to substantially zero the second term of the expression
 
ρ N ∝ρ P +∂ m (∂ x −Z)
 
      where ρ N  is the offered trade object value or price; 
          ρ p . is a desired minimum price, similar to a reserve price;     δ m  is a desired margin value desired by a business operator;     δ x  is an Operational function, constituted of at least a first one of a selected trade indicator; and     Z is the Transaction Driver function, constituted of at least a second one of a selected trade indicator.        

      Thus, in the example where δ x ≅Z, ρ N ≅ρ p . Operational function, δ x , may vary price, ρ i , generally between desired ceiling price ┌ω┐  1125  and desired floor price └α┘  1115 , perhaps urging price ρ i  toward desired mean trade offer value μ  1145 . During a trading event, price ρ i  also may be provided within an envelope of values generally defined within the range of upper envelope bound ξ  1130  and lower envelope bound β  1120 , where the envelope generally tends toward desired mean trade offer value μ  1145 . It is to be understood that upper envelope bound ξ  1130 , lower envelope bound β  1120 , mean trade offer value μ  1145 , and trade offer price, or value, ρ i , may correspond to an Operational function, δ x , that is linear, nonlinear, or a combination thereof. There is no constraint that requires price ρ N  to instantaneously drop to ρ p . Instead, ρ N  may decline in accordance with the manner in which the constituent trade indicators and dimensions of Operational function δ x  and Transaction Driver function Z provide. It is desirable, when Z=δ x , that the signal value representative of special trading event is communicated.  
      During a special trading event, trade object price ρ i  may decrease at an essentially constant rate, at a stochastically variable rate, or at an inventory-dependent rate. The rate of change of ρ i  can be adapted, in some instances in real-time or near-real time, to be responsive to aggregate buyer response and pertinent trade indicators. As the trade object price declines, e.g., from ρ 2  to ρ 3 , a first prospective buyer may be eager to purchase a trade object at price ρ 3  which is higher price than ρ N , and so indicates this desire by transmitting back to the seller a COMMIT token corresponding to the higher trade object value of ρ 3 . By sending a COMMIT token, a prospective buyer tends to decrease trade object inventory by the number of trade objects corresponding to the COMMIT token. In general, q 2 &lt;q 1 .  
      A second prospective buyer may indicate an acceptance of the sellers&#39; offer to purchase by transmitting a COMMIT token after the first prospective buyer, with the second buyer&#39;s COMMIT token corresponding to an accepted trade object price or value ρ 4 , generally lower than the trade object value ρ 3 . accepted by the first prospective buyer. This second prospective buyer, too, decreases available trade object inventory. Likewise, in general, q 3 &lt;q 2 . As the trade object price ρ i  continues to decline, additional prospective purchasers indicate a desire to purchase a trade object by transmitting respective tokens to the seller, with additional respective reductions in trade object inventory, in general q L &lt;q u .  
      Upon the putative exhaustion of inventory, i.e., when trade object inventory reaches quantity q N , the special trading interval, and the trading event defined over interval Δ N , terminates. In desirable embodiments herein, all prospective buyers who committed to purchase a trade object during the special trading event complete the purchase at the final trade object price ρ N , even if the trade object price ρ U  at which the respective purchaser transmitted their COMMIT token was higher than final trade object price ρ N . Such a feature can create an “avalanche” effect with buyers, wherein as prices decline, the number of prospective buyers committing to a purchase increases.  
      By waiting until trade object inventory is exhausted, or nearly so, a prospective purchaser risks not being able to purchase a trade object at all. However, if a prospective purchaser commits to purchase a trade object at the beginning of the special trading event, that purchaser pays no more than the lowest price. In fact, this lowest price is paid by all. The magnitude of final trade object price ρ N  is generally a function of the existant price when inventory exhaustion, or quantity q N  is reached. Prospective buyers may be motivated by the perception to purchase a trade object at a value favorable to the purchaser, by the excitement generated by the trading event, by the nature of the trade object itself, such as a rare collectible, or by a myriad of factors within the personal knowledge of the prospective buyer. Unlike a Dutch auction where each bidder agrees to buy an item at the bid price and bidding continues until inventory exhaustion or the seller opts to halt the auction to preserve pricing structure, the method herein allows all buyers to take at the final offered trade object price, which was in effect at the predetermined trade event termination, here the exhaustion of an inventory of q n  trade objects.  
      Although in the foregoing example, ρ N  declined to ρ p  where Transaction Driver function Z was adapted to approximately equal Operational function δ x , it also is possible that Z can be adapted to have a magnitude greater than δ x , such that the final price ρ N  is less than desired minimum price ρ p . Such adaptation may be useful where inventory clearance becomes a priority. In an extreme instance ρ N =0, i.e., the trade object is being given away. On the other hand, it also is possible to adapt function Z to maintain a magnitude less than Operational function δ x . In certain circumstances, it may even be desirable to provide a selected trade indicator or a combination of selected trade indicators such that Transaction Driver function Z is given a negative value, thereby allowing ρ N &gt;&gt;ρ p . Such an increasing price may be desirable, for example, where buyer activity may exceed what is considered to be acceptable to the seller or business operator or, perhaps on a longer time scale as with a demographic trend, to raise a trade object offer price to accommodate a perceived increase in trade object market value. Again, Transaction Driver function Z and Operational function δ x , may be constituted of selected trade indicators and trade dimensions, which can be combined to provide a desired rate of adaptation for a single trading event, for an ensemble of trading events, for aggregations of trading event ensembles, and the like.  
      Nevertheless, exemplary embodiments of the present invention evoking the perception of free-falling prices for a desirable trade object, can be useful for inventory clearance or reduction, for market introduction of new products or vendors, for generation of service or brand awareness, and so forth. Advantageously, purchases under such circumstances can provide consumer, market, and competitor-related business intelligence, in real time during the trading event, in near-real time, or in retrospect. Such data can be directed to influence Transaction Driver function Z, and can be tailored for a particular type of product, communication channel, geographic and demographic factors, and current consumer and market trends. Such data also can provide valuable enterprise intelligence, also on a real-time, a near-real-time, or a retrospective basis, assisting the enterprise to beneficially adapt to its trading milieu.  
      While the present invention has been described with respect to particular physical embodiments, the invention is not limited to the particulars described above; instead, the scope of the invention is defined by the following claims.