bidder preferences among auction institutions i introduction auctions have become a pervasive method of exchange in the online world as each day thousands of auctions take place online and this trade volume totals to billions of dollars worth of goods per year 1 this large volume of auction transactions implies the existence of a large number of sellers competing for buyers the obvious implication is that the competition among the sellers for the pool of potential buyers can be fierce and any competitive edge a seller can find could be important one such competitive edge a seller might exploit is using an auction design that attracts bidders away from their competitors when designing a real auction or modeling a theoretical one the entry decision of prospective bidders is rarely considered most auction analysis is performed assuming that a certain number of bidders will participate for certain or perhaps that the number of bidders is unknown and randomly determined it should be clear however that the most crucial part of a successful auction is encouraging as many bidders as possible to participate in general this should be expected to have a positive effect on revenue at least in noncommon value environments and in certain types of auctions it may help combat the possibility of bidder collusion because there are typically competing auctions available for similar goods or even outside options that bidders can pursue when auctions are for unique goods it is important to understand how the aspects of an auction format can effect the entry decision of a bidder consider a bidder who is faced with the choice of entering one of two auctions for similar or even identical objects how does this bidder make the decision of which auction to enter the obvious answer is that the bidder will enter into the auction that maximizes his or her expected utility so long as that expected utility is greater than some reservation value the real question then is how are these expected utilities constructed profit from participating in the auction is an obvious argument there are also a number of environmental considerations that might effect this decision that would be difficult to account for precisely such as the reputation and trustworthiness of the auctioneer quality of the advertisement for the auction and things of this nature it is also possible that the format of the auction itself can have an impact on the preferences of the bidder this latter point will be the issue of this study the particular focus will be looking at bidder preferences between the two most common standard auction formats used in the field the sealed bid first price will be abbreviated as just the sealed bid auction and the ascending or english auction the other reason we are interested in comparing these two auction formats rather than the ascending and second price or first price and descending is that it seems reasonable to expect bidders to have preferences between the two due to the strategic differences between them such differences lead to substantial differences in terms of the difficulty of deciding how to bid and also in the possibility that an outcome leads to a bidder experiencing some form of regret regret may occur in a first price auction when a bidder loses to a bid that is below his value as he may think that if only he had bid higher he could have won although such feelings of regret may be considered irrational that does not preclude their existence such a scenario should not reasonably occur in an ascending auction if one considers the situation of a bidder choosing between two auctions that differ only in regard to whether the auction is being conducted according to an ascending or sealed bid format it is not immediately obvious which would be the most preferred even assuming a standard symmetric independent private values environment were all bidders risk neutral then of course revenue equivalence would hold and the bidders would be indifferent

irrationality and ambiguity in extensive games abstract based on a model where deviations from equilibrium play are assumed to identify irrational players who are characterized by ambiguous set valued strategies this paper introduces an equilibrium notion for extensive games with ambiguity averse players that yields a precise interpretation for the counterfactual reasoning usually associated with backward induction the resulting equilibria are always nash equilibria but may not satisfy the conditions required for various refinements of nash equilibrium including those for subgame perfection existence of such equilibria is proved for all two player games and for n player games with perfect information

equilibrium in auctions with entry the authors model entry incentives in auctions with risk neutral bidders and characterize a symmetric equilibrium in which the number of entrants is stochastic the presence of too many potential bidders raises coordination costs that detract from welfare the authors show that the seller and society can benefit from policies that reduce market thickness i e the relative abundance of buyers their analysis extends well known revenue equivalence and ranking theorems but also demonstrates that variations in the auction environment affect optimal policies e g reservation prices in ways not anticipated by models that ignore entry copyright 1994 by american economic association

non additive beliefs and strategic equilibria abstract this paper studies n player games where players beliefs about their opponents behaviour are modelled as non additive probabilities the concept of an equilibrium under uncertainty which is introduced in this paper extends the equilibrium notion of dow and werlang 1994 j econom theory 64 305 324 to n player games in strategic form existence of such an equilibrium is demonstrated under usual conditions for low degrees of ambiguity equilibria under uncertainty approximate nash equilibria at the other extreme with a low degree of confidence maximin equilibria appear finally robustness against a lack of confidence may be viewed as a refinement for nash equilibria journal of economic literature classification numbers c72 d81

how valuable is a good reputation a sample selection model of internet auctions on the online auction site ebay by convention sellers do not ship goods to winning bidders until after they have received payment so there is an opportunity for sellers to take advantage of bidders trust realizing this the designers of ebay created a system that relies on self enforcement using reputation several recent studies have found that bidders give little or no reward to sellers who have better reputations i show that in fact sellers are strongly rewarded for the first few reports that they have behaved honestly but marginal returns to additional reports are severely decreasing

economic insights from internet auctions this paper surveys recent studies of internet auctions four main areas of research are summarized first we survey several studies that document and attempt to explain the frequently observed sniping or last second bidding behavior in these auctions second we summarize several methods proposed to quantify the distortions caused by asymmetric information in these markets most notably due to the winner s curse third we explore research about the role of reputation mechanisms installed to help combat these distortions finally we discuss what internet auctions have to teach us about auction design

equilibrium bid functions for auctions with an uncertain number of bidders abstract the number of rivals may be unknown when a bidding strategy is formulated in an auction in a symmetric model with risk neutral bidders holding independent information we obtain explicit equilibrium bidding functions for first price and second price auctions with uncertainty about the number of rivals five auctions are revenue equivalent first price and second price auctions each with the number of bidders known or uncertain and english auctions

selling online versus live a seller choosing between auctioning online and live faces a tradeoff lower transaction costs online against more rents left with the bidders we model this tradeoff and apply the theory to auctions of art the crucial parameter for whether the seller does better online than live is not the expected price but the valuation uncertainty

extensive form games with uncertainty averse players abstract nash equilibrium presumes that the beliefs of a player are represented by a probability measure motivated by the ellsberg paradox and relevant experimental findings demonstrating that this representation of beliefs may be unrealistic this paper generalizes nash equilibrium in finite extensive form games to allow for preferences conforming to the multiple priors model developed by gilboa and schmeidler journal of mathematical economics 18 1989 141 153 the implications of this generalization for strategy choices and welfare are studied journal of economic literature classification numbers c72 d81

interim efficient allocations under uncertainty abstract this paper considers an exchange economy under uncertainty with asymmetric information uncertainty is represented by multiple priors and posteriors of agents who have either bewley s incomplete preferences or gilboa schmeidler s maximin expected utility preferences the main results characterize interim efficient allocations under uncertainty that is they provide conditions on the sets of posteriors thus implicitly on the way how agents update the sets of priors for non existence of a trade which makes all agents better off at any realization of private information for agents with the incomplete preferences the condition is necessary and sufficient but for agents with the maximin expected utility preferences the condition is sufficient only a couple of necessary conditions for the latter case are provided

correlated equilibrium as an expression of bayesian rationality if it is common knowledge that the players in a game are bayesian utility maximizers who treat uncertainty about other players actions like any other uncertainty then the outcome is necessarily a correlated equilibrium random strategies appear as an expression of each player s uncertainty about what the others will do not as the result of willful randomization use is made of the common prior assumption according to which differences in probability assessments by different individuals are due to the different information that they have where information may be interpreted broadly to include experience upbringing and genetic makeup copyright 1987 by the econometric society

5 information impact and allocation rules in auctions with affiliated private values a laboratory study in affiliated private value auctions each bidder has perfect information regarding his her own value for the object at auction but higher values of the item for one bidder make higher values for other bidders more likely we report on a series of experiments examining three key implications of these auctions i in a first price auction public information about rivals values increases expected revenue ii an english auction increases expected revenue compared to a first price auction and iii a second price auction is isomorphic to an english auction in examining these issues we compare predictions of some ad hoc bidding models with nash equilibrium predictions in the first price auction experiments nash equilibrium bidding theory organizes the data better than either of two ad hoc bidding models public information about others valuations does increase average revenue but the increase in revenue is smaller and less reliable than predicted under risk neutral nash equilibrium bidding lower average revenue might be attributed to risk aversion while the high variability is attributed to a sizable frequency of individual bidding errors relative to the theory bidding theory precisely organizes english auction outcomes after a brief initial learning period the dominant strategy equilibrium does not organize second price auctions nearly as well as market prices persistently exceed predicted prices the difference between english and second price outcomes is attributed to effects of different information flows inherent in the structure of the two institutions on eliminating bidding errors revenue impacts of these two institutions relative to a first price auction are examined in light of observed bidding patterns

an inventory system with demand dependent on both time and price assuming backlogged shortages abstract in this work we analyze an inventory model for items whose demand is a bivariate function of price and time it is supposed that the demand rate multiplicatively combines the effects of a time power function and a price logit function the aim is to maximize the profit per time unit assuming that the inventory cost per time unit is the sum of the holding shortage ordering and purchasing costs an algorithm is developed to find the optimal price the optimal lot size and the optimal replenishment cycle several numerical examples are introduced to illustrate the solution procedure

mechanism design by competing sellers a dynamic model with many sellers and buyers is constructed agents failing to trade may trade in the next period an equilibrium is found where sellers hold identical auctions and buyers randomize over the sellers they visit the distribution of buyer valuations is endogenous an auction with efficient reserve is an optimal mechanism from each seller s point of view in spite of the ability of any seller to alter the distribution of buyer types participating in the seller s mechanism by altering the mechanism copyright 1993 by the econometric society

pennies from ebay the determinants of price in online auctions this paper presents an exploratory analysis of the determinants of prices in online auctions for collectible united states one cent coins at the ebay web site starting with an initial data set of 20 000 auctions we perform regression analysis on a restricted sample of 461 coins for which we obtained estimates of book value we have three major findings first a seller s feedback ratings reported by other ebay users have a measurable effect on her auction prices negative feedback ratings have a much greater effect than positive feedback ratings do second minimum bids and reserve prices have positive effects on the final auction price in particular minimum bids appear only to have a significant effect when they are binding on a single bidder as predicted by theory third when a seller chooses to have her auction last for a longer period of days this significantly increases the auction price on average

the dynamics of seller reputation evidence from ebay we construct a panel of ebay seller histories and examine the importance of ebay s reputation mechanism we find that when a seller first receives negative feedback his weekly sales rate drops from a positive 7 to a negative 7 subsequent negative feedback ratings arrive 25 more rapidly than the first one and don t have nearly as much impact as the first one we also find that a seller is more likely to exit the lower his reputation is and that just before exiting sellers receive more negative feedback than their lifetime average we consider a series of theoretical models and measure them against these empirical results regardless of which theoretical model best explains the data an important conclusion of our paper is that ebay s reputation system gives way to noticeable strategic responses from both buyers and sellers

competition among sellers who offer auctions instead of prices abstract in this paper we study a large market in which sellers compete by offering auctions to buyers instead of simple fixed price contracts two variants of the model are studied one extends a model first analyzed by wolinsky rev econ stud 55 1988 71 84 in which buyers learn their valuations only after meeting sellers the other variant extends the model of mcafee econometrica61 1993 1281 1312 in which buyers know their valuations before they choose among available auctions the equilibrium array of auctions is characterized for each case and the efficiency properties of the equilibria are analyzed journal of economic literatureclassification numbers d41 d44 d82

risk ambiguity and the rank dependence axioms choice problems in the spirit of ellsberg 1961 suggest that rank dependent choquet expected utility preferences over subjective gambles might be subject to the same difficulties that ellsberg s earlier examples posed for subjective expected utility these difficulties stem from event separability properties that rank dependent preferences partially retain from expected utility and suggest that nonseparable models of preferences might be better at capturing features of behavior that lead to these paradoxes

a more robust definition of subjective probability the goal of choice theoretic derivations of subjective probability is to separate a decisionmaker s underlying beliefs subjective probabilities of events from their preferences attitudes toward risk classical derivations have all relied upon some form of the marschak samuelson independence axiom or the savage sure thing principle which imply that preferences over lotteries conform to the expected utility hypothesis this paper presents a choice theoretic derivation of subjective probability in a savage type setting of purely subjective uncertainty which neither assumes nor implies that the decisionmaker s preferences over lotteries necessarily conform to the expected utility hypothesis copyright 1992 by the econometric society

uncertainty aversion in game theory experimental evidence abstract this paper studies using a laboratory experiment the effects of uncertainty aversion the union of risk aversion and ambiguity aversion on behavior in a normal form game we isolate and identify two components of uncertainty aversion in games the effect of an agent s own uncertainty preferences and effect of the agent s beliefs regarding their opponent s uncertainty preferences uncertainty preferences are correlated with behavior in games induced beliefs about the risk preferences of an opponent have a larger effect on strategic behavior than induced beliefs about an opponent s ambiguity preferences although both components have a significant effect on behavior the results support the hypothesis that strategic uncertainty is an important determinant of strategic behavior and that the response to strategic uncertainty is modulated by subject uncertainty attitudes

collusion and the choice of auction auctions are used in many different markets including the leasing of a substantial fraction of the natural resources in the united states the procedures used in the auctions conducted by the federal government have been a continuing source of controversy one of the concerns has been the possibility of collusion among bidders this article shows that cartels are stable if the seller uses open ascending bid oral auctions but not if he uses sealed high bid auctions this may help to explain the frequent use of sealed high bid auctions

nash equilibrium under knightian uncertainty breaking down backward induction abstract we define nash equilibrium for two person normal form games in the presence of knightian uncertainty using the formalization of schmeidler and gilboa we show that nash equilibrium exists for any degree of uncertainty aversion that maxmin behaviour can occur even when it is not rationalizable in the usual sense and that backward induction breaks down in the twice repeated prisoners dilemma we relate these results to the literature on cooperation in the finitely repeated prisoners dilemma and the literature on epistemological conditions underlying nash equilibrium the knowledge notion implicit in this model of equilibrium does not display logical omniscience journal of economic literature classification numbers c72 d81

identification of standard auction models this paper presents new identification results for models of first price second price ascending english and descending dutch auctions we consider a general specification of the latent demand and information structure nesting both private values and common values models and allowing correlated types as well as ex ante asymmetry we address identification of a series of nested models and derive testable restrictions enabling discrimination between models on the basis of observed data the simplest model symmetric independent private values is nonparametrically identified even if only the transaction price from each auction is observed for richer models identification and testable restrictions may be obtained when additional information of one or more of the following types is available i the identity of the winning bidder or other bidders ii one or more bids in addition to the transaction price iii exogenous variation in the number of bidders iv bidder specific covariates while many private values pv models are nonparametrically identified and testable with commonly available data identification of common values cv models requires stringent assumptions nonetheless the pv model can be tested against the cv alternative even when neither model is identified

optimism and pessimism in games this paper considers the impact of ambiguity in strategic situations it extends the earlier literature by allowing for optimistic responses to ambiguity ambiguity is modelled by ceu preferences we propose a new solution concept for players who may express ambiguitypreference then we study comparative statics of changes in ambiguity attitude in games with strategic complements this gives a precise statement of the impact of ambiguity on economic behaviour

correlated nash equilibrium abstract we modify the epistemic conditions for nash equilibrium only to accommodate gilboa and schmeidler s i gilboa d schmeidler maxmin expected utility with nonunique prior j math econ 18 1989 141 153 maxmin expected utility preferences and identify the equilibrium concept in n player strategic games that characterizes the modified epistemic conditions the epistemic characterization supports the equilibrium concept as a minimal generalization of nash equilibrium in the sense that it deviates from nash equilibrium only in terms of players attitude towards ambiguity consequently comparing it with nash equilibrium constitutes a ceteris paribus study of the effects of ambiguity on how a game is played for example with ambiguity beliefs about action choices are in general correlated

estimation of beauty contest auctions beauty contests are auction mechanisms used to buy or sell differentiated products where the auctioneer does not specify a decision rule to pick the winning bidder beauty contests are widely used in procuring welfare to work projects freelance services selling online ads real estate transactions and hiring dating marriage decisions unlike price only auctions beauty contests have no closed form bidding strategies and suffer from nonmultiplicatively separable unobserved auction heterogeneity which makes their estimation challenging to address these challenges we formulate beauty contests as incomplete information games and present a two step estimator a key contribution of our method is its ability to account for common knowledge auction specific unobservables using finite unobserved types we show that unobserved auction types and distributions of bids are nonparametrically identified and recoverable in the first step using a nonparametric expectation maximization em like algorithm and that

a definition of uncertainty aversion a definition of uncertainty or ambiguity aversion is proposed it is argued that the definition is well suited to modelling within the savage as opposed to anscombe and aumann domain of acts the defined property of uncertainty aversion has intuitive empirical content behaves well in specific models of preference multiple priors and choquet expected utility and is tractable tractability is established through use of a novel notion of differentiability for utility functions called eventwise differentiability

sealed bid versus open auctions the evidence data from u s forest service timber auctions are used to test vickrey s original proposition that sealed bid and open auctions yield equal revenue models for the high bid in an auction are specified and estimated using three different procedures ordinary least squares two stage least squares and maximum likelihood the second two procedures include a second equation which accounts for the forest service s auction choice and therefore control for selection bias these two procedures which unlike ordinary least squares yield consistent estimators imply a statistically and economically insignificant difference in high bids between sealed bid and open auctions

hedonic prices and implicit markets estimating demand and supply functions for differentiated products in choosing the level of quality to purchase the buyer of a differentiated product also chooses a point on the marginal price schedule for that product hence in general the demand functions for product characteristics cannot be consistently estimated by ordinary least squares market equilibrium results in a matching of characteristics of demanders and suppliers this matching restricts the use of buyer and seller characteristics as instruments when estimating demand and supply functions for product characteristics the paper develops these issues a stochastic structure for hedonic equilibrium models is then proposed identification results are presented and estimation procedures are outlined

bidding off the wall why reserve prices may be kept secret abstract this note shows by means of an example that in a common value auction a seller with a random reservation value can increase her ex ante expected profits by following a policy of conducting an auction in which her reserve price is kept secret compared to an auction in which the reserve price is announced by keeping the reserve price secret the seller is able to encourage greater participation from the bidders and can therefore increase the linkage of the price paid to the value of the purchased object journal of economic literature classification numbers d82 d44

vickrey auctions in practice from nineteenth century philately to twenty first century e commerce william vickrey 1961 proposed an auction mechanism in which bidders submit sealed bids and the highest bidder wins the good in return for payment of the second highest bid amount for decades economists have credited vickrey with inventing this auction format and have believed that the vickrey auction is rarely used in practice this paper presents evidence that vickrey auctions have long been the predominant auction format for mail sales of collectible postage stamps stamp auctioneers developed this auction format on their own as early as 1893 even before vickrey was born