Abstract:
A trading system employing an adaptive stochastic transaction system is provided in which a first party is disposed to propose an object offer to a second party, which is disposed to accept the object offer. A marketing communication link couples the vendor and the vendee, whereby the vendor and the vendee communicate data relative to an object offer. A distribution channel may be incorporated for providing a perceivable indication of the object to be offered so that the vendor may propose the object offer to the vendee through the communication link and wherein the data relative to an object offer includes a quasi-stochastic tuple related to the offer value and wherein the vendee is induced to accept the object offer having the offer value being one of generally equal to and less than the purchase value.

Description:
CROSS-REFERENCE TO RELATED APPLICATION  
       [0001]     This is an ordinary application of provisional application Ser. No. 60/689,307, filed Jun. 10, 2005, the contents of which are expressly incorporated herein by reference as if set forth in full. 
     
    
       [0002]     A trading system employing an adaptive stochastic transaction system is provided in which a first party is disposed to propose an object offer to a second party, which is disposed to accept the object offer.  
       BACKGROUND  
       [0003]     Trading systems are well known in the art and include eBay and the QVC home shopping network. Generally speaking, a trading system consists of a first party offering an object to a second party, which has the option of accepting the offered object at the offered price. The offered price may be a fixed price, an upwardly trending price sold to a highest bidder (English auction), a sealed-bid auction, or a downwardly trending price (Dutch auction). A trading system not only provides a useful service or function, by providing a transaction medium between two different parties, it is part entertaining as it provides a stimulating and enjoyable experience.  
         [0004]     Although the prior art trading systems are effective and have generated millions if not billions in annual sales, they do not include a stochastic element over communication channels for conducting a transaction as described herein.  
       SUMMARY  
       [0005]     The present invention may be implemented by providing a trading system comprising: a computer for establishing an offer value for an object offer, said offer value includes a quasi-stochastic tuple related to the establishment of the offer value; a database for processing a response linked to the object offer at the offer value; and a marketing communication link for conveying the object offer at the offer value.  
         [0006]     Another aspect of the invention includes a transaction system for conducting an exchange for value comprising: a computer terminal comprising a controller for computing a plurality of sets of offer value and offer interval for an object offer, including a first set and a second set, wherein at least one of the offer value and offer interval within a set falls within a distribution envelope that is shaped, at least in part, by a probability distribution function; and wherein at least one of the offer value and offer interval within a set varies from an offer value and an offer interval within a different set by a value having a randomized factor; and a marketing communication link for receiving a first response token and a second response token linked to the first set and the second set.  
         [0007]     In still other aspects of the present invention, there is provided a method for conducting a transaction comprising: offering a first object for transacting; computing a first offer value and a first offer interval for making the transaction involving the first object; receiving a response for the first object; offering a second object for transacting; computing a second offer value and a second offer interval for making the transaction involving the second object; facilitating the first set and the second set to be displayed on at least one of a broadcast network and a wide area communication network; receiving a response for the second object; and wherein at least one of the second offer value and the second offer interval differ from the first offer value and the first offer interval by a factor computed by a stochastic process.  
         [0008]     In yet other aspects of the present invention, there is provided a trading system employing an adaptive stochastic transaction system in which a first party is disposed to propose an object offer to a second party, which is disposed to accept the object offer. A marketing communication link couples the vendor and the vendee, whereby the vendor and the vendee communicate data relative to an object offer. A distribution channel is incorporated for providing a perceivable indication of the object to be offered so that the vendor may propose the object offer to the vendee through the communication link and wherein the data relative to an object offer includes a quasi-stochastic tuple related to the offer value and wherein the vendee is induced to accept the object offer having the offer value being one of generally equal to and less than the purchase value.  
         [0009]     In still yet another aspect of the present invention, there is provided a a transaction system comprising: an event inventory comprising an object total, a computer for establishing a first offer value for each object in a first plurality of objects to be offered during a first offer interval and for establishing a subsequent offer value for each object in a subsequent plurality of objects to be offered during a subsequent offer interval; a marketing communication link for conveying the first plurality of objects at the first offer value over the first offer interval and for conveying the subsequent plurality of objects at the subsequent offer value over the subsequent offer interval to a plurality of vendees; a database for processing a plurality of responses linked to the first plurality of objects and the subsequent plurality of objects; an executable program for adjusting a running number of object total, which is the object total less the first plurality of objects and the subsequent plurality of objects plus a number of canceled objects; and wherein the marketing communication link comprises an Internet link and a telephone network.  
         [0010]     Other aspects and variations of the transaction systems summarized above are also contemplated and will be more fully understood when considered with respect to the following disclosure. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0011]     These and other features and advantages of the present invention will become appreciated as the same become better understood with reference to the specification, claims and appended drawings wherein:  
         [0012]      FIG. 1  represents a first exemplary embodiment of adaptive, stochastic transaction system provided in accordance with aspects of the present invention;  
         [0013]      FIG. 2  illustrates a business-to-consumer enterprise or transaction system as provided in accordance with aspects of the present invention  
         [0014]      FIG. 2A  is a pictorial representation of a multimodal, bi-directional communication channel capable of multimedia transmissions for implementing the transaction system in accordance with aspects of the present invention;  
         [0015]      FIG. 3  is a graphical representation of a time-domain mapping of a trading event provided in accordance with a first aspect of the present invention;  
         [0016]      FIG. 4  is a graphical representation of a time-domain mapping of a trading event provided in accordance with a second aspect of the present invention, which includes at least one stochastic dimension; and  
         [0017]      FIG. 5  is yet another mapping of a time-domain mapping of a trading event provided in accordance with another aspect of the present invention, which includes a plurality of stochastic dimension processes. 
     
    
     DETAILED DESCRIPTION  
       [0018]     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 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 later case, the actual exchange is initially deferred and later completed by one or more ancillary communications or transfers.  
         [0019]     A stochastic decision token includes at least one attribute, property, or value (collectively, 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, pseudo-stochastic and pseudo-random features, as well as quasi-stochastic and quasi-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-talking, efficiency, error, Shannon entropy, and the like.  
         [0020]     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.  
         [0021]      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 uplink  140 , 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  to solicit a response Φ  170 . 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 for future offers  180  may be difficult to predict on the basis of past values. This unknown property may be perceived by some as an element of risk. Although difficult prediction of future values, and financial risks, may be undesirable to some persons in certain 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 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.  
         [0022]      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 bi-directional 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, bi-directional 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, it 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 .  
         [0023]      FIG. 2A  is a pictorial representation of a multimodal, bi-directional communication channel capable of multimedia transmissions, generally represented as  10 . In one exemplary embodiment, an uplink  215  for communicating a stochastic decision token by a first party or seller to one or more buyers or second parties comprises a broadcast network  12  by which a video presentation of a transaction is televised. Input to the broadcast network  12  may be from a seller&#39;s hub  14  by way of an optical transfer medium  16 , such as an optic cable. The seller may also broadcast or provide an uplink  215  using a packet-switched communications internetwork using a server  18  connected to the Internet  20  and/or a public switched network facilitating point-to-point communication with its hub  14 . A buyer may communicate a return response using a personal computer  22 , a land telephone  23 , a cell phone  24 , a handheld computer  26 , or a fax machine  28  to commit to a transaction (or to cancel a prior committed order as further discussed below).  
         [0024]     The adaptive stochastic transaction system discussed elsewhere herein may be implemented on the server  18  and include a database for linking stochastic decision tuples with corresponding response tokens. Existing prior art registration systems may be incorporated to authenticate vendees or buyers and for registering the same.  
         [0025]     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 seller  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 a 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 .  
         [0026]     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.  
         [0027]     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     ⁢     δ   i           
 
         [0028]     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.  
         [0029]     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, marketgoers 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.  
         [0030]     Nevertheless, motivated observers may seek for 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.  
         [0031]     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 , is of little or no value.  
         [0032]     Generally, one aspect of the preselected trading protocol involves seller  205  signalling 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 . 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 .  
         [0033]     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 χ  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 χ response  250 , by which a made transaction subsequently is repudiated. In this particular embodiment, both COMMIT Π i  or CANCEL χ 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 , shown as a repeat offer  260  based on a different stochastic decision tuple, to buyer  210 .  
         [0034]     To seller  205 , the preselected trading protocol includes signaling buyer  210  with stochastic decision tuple &lt;δ i ,ρ i &gt;  225 , awaiting 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 .  
         [0035]     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 a CANCEL value χ, 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. 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.  
         [0036]     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. Accessing seller&#39;s transaction system should include a registration process, such as providing a name, a mailing address, requesting a user ID and password, and registering a payment option (e.g., credit card information). If buyer has previously registered, an IP address or a telephone ID may be used to link buyer with a registered purchaser. 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.  
         [0037]     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 χ.  
         [0038]      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 (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    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 . 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).  
         [0039]     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  
 
         [0040]     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     ⁢     δ   i           
 
         [0041]     Trading 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.  
         [0042]     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 value 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 [c)]  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.  
         [0043]     Process  300  generates 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 P(x). In general, the PRNG device or technique generates randomized values corresponding to a dimension; the selected probability distribution function P(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 P(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 P(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 P(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 .  
         [0044]     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 1    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 remains unterminated, 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  interval of event interval Δ N    315 , final offer value ρ N    355  also is revoked, and uncancelled, 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.  
         [0045]     Selected embodiments also provide seller  205  with the ability to interject promotional offer value ρ p  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.  
         [0046]      FIG. 4  also is a mapping representative of possible outcomes of stochastic dimension 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    402  for a defined trading event. Trading interval Δ N    402  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 P(x) to shape the randomized range of values output by a PRNG, a definable subspace of possible RPNG outcomes generally may be approximated by a preselected distribution envelope described by probability distribution function P(x).  
         [0047]     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 P(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 Q(x), where (P(x)≠Q(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).  
         [0048]     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 . 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  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 Q(x) to vary generally between predetermined minimum offer interval δ L    485  and predetermined maximum offer interval δ U    490 . Probability distribution function Q(x) can be selected such that the corresponding distribution envelope of the offer interval δ i  substantially conforms to the sample subspace desired.  
         [0049]     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, P(x) and Q(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.  
         [0050]     Unlike process  300  in  FIG. 3 , embodiments according to process  400  in  FIG. 4  may possess an adapted mean value 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 P(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 Q(x) such that offer intervals δ i  are generated within an exemplary Gaussian distribution envelope instead of an exemplary Uniform distribution. Distribution function Q(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 extreme of the distribution envelope representative of distribution function P(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 P(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.  
         [0051]      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, quasi-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 .  
         [0052]     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 show). 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.  
         [0053]     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 ε 1 , ε 2 , . . . , ε 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 ε 1 , ε 2 , . . . , ε M . Ensemble members ε 1 , ε 2 , . . . , ε 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 ε i , which itself may include suitable PRNG to generate values of &lt;δ i ,ρ i &gt; using functions Q(x) and P(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 ε i , as is illustrated in  FIG. 5 . In certain embodiments, one ensemble member ε may be provided for each offer interval δ i  in trading interval  502 . In others, there may be fewer ensemble members ε than offer intervals δ i . In such a case, it is desirable to re-use ensemble member functions ε, so that member functions ε 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 ε. 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 quasi-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, Gaussion, 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.  
         [0054]     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 ε 5  generates first stochastic decision tuple &lt;δ i ,ρ i &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 δ 1  expires. Prior to the expiration of first offer interval δ 1 , ensemble member process ε 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 signalled 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 ε 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 ε 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 P  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 .  
         [0055]     Exemplary implementation of certain aspects of the present invention includes a transaction system in which a stochastic decision tuple  225  is uplinked over a broadcast network and a packet-switched communications internetwork (i.e., the Internet). In one specific example, one hundred ( 100 ) digital cameras are offered over a trading interval Δ comprising  100  offer intervals δ 1-100  each linked to offer values ρ 1-100 . Assuming a first digital camera is being offered at $400 if accepted over the next 3 minutes, a viewer-purchaser watching the trading event on television may quickly act on the offer, because it lower than a manufacturer&#39;s suggested retail value, by picking up a telephone and dialing seller&#39;s circuit-switched network and depressing a telephone key, such as an asterisk key to COMMIT. The first offer event may include a plurality of cameras offered at $400 over a first time interval as the audience may include a plurality of viewers or participants. However, for the sake of convenience, further discussions only relate to a single item being offered during an offer event over an offer interval although it is understood that more than one items (e.g., two or more cameras) may be offered for an offer value over an offer interval. The number of items being offered per offer interval may be established prior to the first offer interval or during the trading interval Δ N  with the trading event inventory or total trade object inventory being a factor.  
         [0056]     When a second stochastic decision tuple is offered, the camera may be offered for more, if the offer interval during the prior offer hardly elapsed, for less, if the offer interval took almost the whole 3 minute period or if there was a NULL response, or for the same amount. Additionally, the offer price may remain the same, increase, or decrease. During the second trading interval, a purchaser, using the Internet, may click buy to COMMIT to the second offer.  
         [0057]     The third through 100 cameras may proceed the same way until the entire trading event inventory is exhausted. It is possible the trading event may extend beyond 100 trading intervals if, for example, a purchaser provides a response token that includes a CANCELATION. In this case, the trading event may continue for as long as the trading event inventory remains. Alternatively, seller may chose to terminate the trading event early or right at the 100th offer.  
         [0058]     In an exemplary embodiment, a plurality of object offers or items being offered at an offer value during an offer interval may receive a corresponding number of responses from multiple participants or vendees over a plurality of communication sources, such as the Internet, a palm PC with wireless or wireless connection, a desktop PC, a telephone, and a fax machine. Thus, aspects of the present invention include a system capable of receiving, handling, and manipulating simultaneous or substantially contemporaneous responses from multiple communication sources.  
         [0059]     In another application of the stochastic transaction system provided in accordance with aspects of the present invention, a series of decreasing offer values are provided until the entire trading event inventory is exhausted. Thus, in the 100-camera example, a first offer value may be established within a pre-selected ceiling value, which may represent an MSRP, down to a preselected floor value, which may represent seller&#39;s cost-to-market price. As each stochastic decision tuple is offered to a plurality of purchasers, a corresponding response token is received, from a purchaser first to submit a response within the offer interval. To entice additional purchasers, a subsequent offer value and offer interval may both decrease, which will likely elicit a response as the decrease in offer value presents a saving to purchaser. The decrease in offer value and offer interval, while trending downwardly, may be random due to the stochastic nature of either or both the offer value and the offer interval, as discussed above. An earlier purchaser may rejoin the trading event by CANCELING a prior commitment. However, he or she risks missing out on a subsequent purchase due to the rapid nature of the trading event and the competition provided by other purchasers in purchasing a limited event inventory.  
         [0060]     In an alternative embodiment, the preseleted floor value may be lower than seller&#39;s cost of goods. This situation may arise if seller is motivated to sell the entire inventory while basing profits on the average sales of the entire inventory rather than on a per transaction basis. Still alternatively, the cameras or other tangible or intangible goods of value in the trading event inventory may be calculated so that offer values corresponding to each pair of offer value and offer interval in a stochastic decision tupble fall within a pre-selected ceiling value and preselected floor value but within a smaller envelope computed from a preselected non-deterministic process. For example, the cameras may be priced or valued within an adapted upper target offer and an adapted lower target offer because, for example, they are new on the market and difficult to get. Other factors may include geopolitical factors in which additional tariffs are imposed thus making the cameras more expensive and therefore buying at a competitive price more compelling.  
         [0061]     Although limited embodiments of the transaction and trading systems and their components have been specifically described and illustrated herein, many modifications and variations will be apparent to those skilled in the art. For example, a trading event may be limited to over the air broadcasting or CATV uplink and a telephone network downlink, and the items being offered may be other than commodities, they may include services, antiques, specialty items, collectable items, professional services, made to order items, an exchange of one item for value for another item of value, etc. Accordingly, it is to be understood that the transacting and trading systems and their components constructed according to principles of this invention may be embodied other than as specifically described herein. The invention is also defined in the following claims.