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Abstract:
This paper analyzes a two-stage sealed-bid auction that is frequently employed in privatization, takeover, and merger and acquisition contests. This auction format yields the same expected revenue as the open ascending (English) auction, yet is less susceptible to preemptive bidding and collusion.

Abstract:
We consider an augmented version of the symmetric private value auction model with independent types. The augmentation, intended to illustrate reality, concerns information bidders have about their opponents. To the standard assumption that every bidder knows his type and the distribution of types is common knowledge we add the assumption that the ranking of bidders' valuations is common knowledge.

This set-up induces a particular asymmetric auction model that raises serious technical difficulties. We prove existence and uniqueness of equilibrium in pure strategies in the two bidder case. We also show that the model generally has no analytic solution. If the distribution of valuations is uniform, both bidders bid pointwise more aggressively relative to the standard symmetric case. However, this property does not apply to all distributions of valuations. Finally, we also provide a numerical solution of equilibrium bid functions for the uniform distribution case.

Abstract:
While auction research, including asymmetric auctions, has grown significantly in recent years, there is still little analytical solutions of first-price auctions outside the symmetric case. Even in the uniform case, Griesmer et al. (1967) and Plum (1992) find solutions only to the case where the lower bounds of the two distributions are the same. We present the general analytical solutions to asymmetric auctions in the uniform case for two bidders, both with and without a minimum bid. We show that our solution is consistent with the previously known solutions of auctions with uniform distributions. Several interesting examples are presented including a class where the two bid functions are linear. We hope this result improves our understanding of auctions and provides a useful tool for future research in auctions.

asymmetric auctions

Abstract:
In the framework of a first-price private-value auction, we study the seller as a player in a game with the buyers in which he has private information about their realized valuations. We find that depending upon his information, set of signals, and commitment power, he may strategically transmit messages to buyers in order to increase his revenue. In an environment where the seller knows the rankings and lacks any commitment power, we find that the seller is unable to exploit his information. However, in an environment where the seller knows the realized valuations and can credibly announce either the true rankings or the true values (or announce nothing at all) but cannot commit as to which of these truthful messages to announce, then it is indeed possible to increase his revenue. If the seller, in addition, can commit to the full signaling strategy, then his expected revenue will be even higher. We believe that this line of research is fruitful for both better understanding behavior in auctions and finding paths to higher seller revenue.

Information, auctions, information transmission, cheap talk, verifiability

Abstract:
We formulate a way to study whether the asymmetry of buyers (in the sense of having different prior probability distributions of valuations) is helpful to the seller in private-value auctions (asked first by Cantillon [2001]). In our proposed formulation, this question corresponds to two important questions previously asked: Does a first-price auction have higher revenue than a second-price auction when buyers have asymmetric distributions (asked by Maskin and Riley [2000])? And does a seller enhance revenue by releasing information (asked by Milgrom and Weber[1982])? This is shown by constructing two Harsanyi games of incomplete information each having the same ex-ante distribution of valuations but in one beliefs are symmetric while in the other beliefs are sometimes asymmetric. Our main result is that answers to all three questions coincide when values are independent and are related when values are affiliated.

asymmetric auctions, asymmetric beliefs, affiliation, linkage principle

Abstract:
We provide an extension of the Condorcet Theorem. Our model includes both the Nitzan-Paroush framework of "unequal competencies" and Ladha's model of "correlated voting by the jurors". We assume that the jurors behave "informatively", that is, they do not make a strategic use of their information in voting. Formally, we consider a sequence of binary random variables X=(X1,X2,...,Xn,...) with range in {0,1} and a joint probability distribution P. The pair $(X,P)$ is said to satisfy the "Condorcet Jury Theorem" (CJT) if, as n goes to infinity, the probability of having a majority of X's with value 1 goes to one.

For a general (dependent) distribution P we provide necessary as well as sufficient conditions for the CJT. In particular, our results establishes the validity of the CJT for a domain which strictly (and naturally) includes the domain of independent jurors.

Social Choice, Condorcet, Voting, Committee

Abstract:
We present experimental results on the ultimatum bargaining game which support an evolutionary explanation of subjects' behaviour in the game. In these experiments subjects interacted with each other and also with virtual players, i.e. computer programs with pre-specified strategies. Some of these virtual players were designed to play the equitable allocation, while others exhibited behaviour closer to the subgame-perfect equilibrium, in which the proposer's share is much larger than that of the responder. We have observed significant differences in the behaviour of real subjects depending on the type of 'mutants' (virtual players) that were present in their environment.