Dominant strategy implementation in economic environments

We study dominant strategy implementation especially in economic environments. We first show that in general environments, strategy-proofness and quasi-strong-non-bossiness together are necessary and sufficient for dominant strategy implementation via the associated direct revelation mechanism. We next prove that in weak separable environments, strategy-proofness is sufficient for dominant strategy implementation, by using an augmented revelation mechanism similar to the one devised by Jackson, Palfrey, and Srivastava [Jackson, M.O., Palfrey, T.R., Srivastava, S., 1994. Undominated Nash implementation in bounded mechanisms. Games Econ. Behav. 6, 474–501]. Moreover, we focus on pure exchange economies without free disposal, and try to construct another augmented revelation mechanism that satisfies balancedness in and out of equilibrium, and which implements all strategy-proof social choice functions in dominant strategy equilibria.     

Auctions in which losers set the price

We study auctions of a single asset among symmetric bidders with affiliated values. We show that the second-price auction minimizes revenue among all efficient auction mechanisms in which only the winner pays, and the price only depends on the losers' bids. In particular, we show that the kth price auction generates higher revenue than the second-price auction, for all k>2. If rationing is allowed, with shares of the asset rationed among the t highest bidders, then the (t+1)st price auction yields the lowest revenue among all auctions with rationing in which only the winners pay and the unit price only depends on the losers' bids. Finally, we compute bidding functions and revenue of the kth price auction, with and without rationing, for an illustrative example much used in the experimental literature to study first-price, second-price and English auctions.     

Bidder collusion

We analyze bidder collusion at first-price and second-price auctions. Our focus is on less than all-inclusive cartels and collusive mechanisms that do not rely on auction outcomes. We show that cartels that cannot control the bids of their members can eliminate all ring competition at second-price auctions, but not at first-price auctions. At first-price auctions, when the cartel cannot control members’ bids, cartel behavior involves multiple cartel bids. Cartels that can control bids of their members can suppress all ring competition at both second-price and first-price auctions; however, shill bidding reduces the profitability of collusion at first-price auctions.     

A Study of Collusion in First-Price Auctions

This paper examines the bidding for school milk contracts in Florida and Texas during the 1980s. In both states firms were convicted of bid-rigging. The data and legal evidence suggest that the cartels in the two states allocate contracts in different ways: One cartel divides the market among members, while the other cartel also uses side payments to compensate members for refraining from bidding. We show that both forms of cartel agreements are almost optimal, provided the number of contracts is sufficiently large.
In the auction the cartel bidder may face competition from non-cartel bidders. The presence of an optimal cartel induces an asymmetry in the auction. The selected cartel bidder is bidding as a representative of a group and has on average a lower cost than a non-cartel bidder. The data support the predicted equilibrium bidding behaviour in asymmetric auctions in accordance with optimal cartels.     

Equilibrium uniqueness with perfect complements

The present note analyzes the simultaneous ascending-bid auction with arbitrarily many asymmetric bidders with decreasing marginal valuations under complete information. We show that the game is solvable by iterated elimination of weakly dominated strategies if the efficient allocation assigns at least one unit to every player and if bid increments are sufficiently small. In that unique equilibrium, bidders immediately reduce their demand to the efficient allocation, and the auction ends in the first round of bidding.We would like to thank seminar participants at UC Davis, in particular Klaus Nehring and Louis Makowski for comments. Financial support by the Alexander–von–Humboldt Foundation through a Feodor–Lynen grant and by the Deutsche Forschungsgemeinschaft, SFB Transregio 15, “Governance and Efficiency of Economic Systems” is gratefully acknowledged.     

An ascending double auction

We show why the failure of the affiliation assumption prevents the double auction from achieving efficient outcomes when values are interdependent. This motivates the study of an ascending price version of the double auction. It is shown that when there is a sufficiently large, but still finite, number of sellers, this mechanism has an approximate perfect Bayesian equilibrium in which traders continue bidding if and only if their true estimates of the ‘value’ of the object being traded exceed the current price. This equilibrium is ex post efficient and has a rational expectations property in the sense that along the equilibrium path traders appear to have made the best possible trades conditional on information revealed by the trading process. We thank two anonymous referees and Dan Kovenock, the Editor, whose detailed comments and suggestions have allowed us to substantially improve the paper. We also thank seminar participants at University of Toronto, University of Wisconsin-Madison, Summer 2003 North American Meetings of the Econometric Society, 2004 NSF Decentralization Conference for their comments.     

Dissertation abstract: Voting in the laboratory

Almost every week national elections are held somewhere in the world. Many more elections take place at federal and local levels of government. Surely, these are important events to many of us. This thesis aims at providing a better understanding of why and how people vote in elections. Three original modifications of Palfrey and Rosenthal’s (1983) participation game are used to study voter turnout theoretically and experimentally.¹ In the basic game, each voter supports (i.e., prefers) one of two exogenous candidates and privately decides between voting at a cost and abstaining (without costs). The candidate who receives more votes wins the election (ties are broken randomly) and each supporter of this candidate receives an equal reward, independent of whether or not she voted. The first study (published in the American Political Science Review 100, pp. 235–248) analyzes the effects of social embeddedness on turnout, assuming that voters may be influenced by observing the decisions of other voters around them (e.g., a family or working place). Our experimental results show that the social context matters: this information increases turnout by more than 50%. The increase is greater when neighbors support the same candidate rather than when they support opponents. The second study investigates the effects of public opinion polls on voter turnout and welfare. Poll releases resolve uncertainty about the level of support for each candidate caused by `floating’ voters, whose preferences change across elections. This information increases turnout in the laboratory by 28–34%, depending on the fraction of floating voters in the electorate. If polls indicate equal levels of support for both candidates—in which case aggregate benefits for society are not affected by the outcome—welfare decreases substantially due to costs from excessive turnout. In the final study, elections are preceded by the competition between two candidates: they simultaneously announce binding policy offers in which some voters can be favored at the expense of others through inclusion and exclusion in budget expenditure (Myerson 1993).² We observe that policy offers include 33% more voters—yielding a smaller budget share for each—when voting is compulsory rather than voluntary. Moreover, we find evidence of political bonds between voters and long-lived parties. Overall, in all three experiments many subjects strongly react to economic incentives (i.e., benefits, costs, and informational clues), often in line with what is observed outside of the laboratory. JEL Classification C72, C92, D72 Dissertation Committee: Arthur Schram, University of Amsterdam (advisor) Axel Ockenfels, University of Cologne Thomas Palfrey, California Institute of Technology Cees van der Eijk, University of Nottingham Frans van Winden, University of Amsterdam ¹Palfrey, T.R., & Rosenthal, H. (1983). A strategic calculus of voting. Public Choice, 41, 7–53. ²Myerson, R.B. (1993). Incentives to cultivate favored minorities under alternative electoral systems. American Political Science Review, 87, 856–869.     

Auction Design for the Allocation of Emission Permits in the Presence of Market Power

To the extent that emission permits have been allocated using market mechanisms, this has been done using a sealed-bid auction design, typically with discriminatory prices. However, several authors have recommended the ascending auction format. Basically, two competing ascending auction designs have been suggested, the standard ascending auction (with clock or demand schedules), or an alternative ascending-clock implementation of Vickrey-pricing. The latter design was introduced as a response to problems of bid shading under the sealed-bid and the standard ascending auction format. The purpose of this paper is to investigate the allocation of permits under these two alternative mechanisms. The auction process and the resulting market outcome in the presence of oligopolistic competition are simulated. In this setting, it is not obvious that bid shading is the optimal strategy under the standard design, nor is it obvious that sincere bidding is the optimal strategy under the alternative ascending auction design. The alternative auction format makes it less costly to pursue a strategy to increase market shares through the acquisition of emission permits, thus increasing the competitor's costs, leading to overbidding as the optimal strategy.     

Sequential vs. single-round uniform-price auctions

We study sequential and single-round uniform-price auctions with affiliated values. We derive symmetric equilibrium for the auction in which k₁ objects are sold in the first round and k₂ in the second round, with and without revelation of the first-round winning bids. We demonstrate that auctioning objects in sequence generates a lowballing effect that reduces the first-round price. Total revenue is greater in a single-round, uniform auction for k=k₁+k₂ objects than in a sequential uniform auction with no bid announcement. When the first-round winning bids are announced, we also identify a positive informational effect on the second-round price. Total expected revenue in a sequential uniform auction with winning-bids announcement may be greater or smaller than in a single-round uniform auction, depending on the model's parameters.     

FARSIGHTED COALITIONAL STABILITY OF A PRICE LEADERSHIP CARTEL

This paper analyzes the farsighted behaviour of firms that form a dominant price leadership cartel. We consider stability concepts such as the farsighted core, the farsighted stable sets, and the largest consistent set. We show that: (i) the farsighted core is either an empty set or a singleton set of the grand cartel; (ii) any Pareto efficient cartel is itself a farsighted stable set; and (iii) the set of cartels in which fringe firms enjoy higher profits than the firms in the minimal Pareto efficient cartel is the largest consistent set.     

Semicollusion vs. Full Collusion: The Role of Demand Uncertainty and Product Substitutability

We examine the profitability of two different cartel organizational forms: full collusion, under which firms collude on both price and quality, and semicollusion, under which firms collude on price only. We show that, in the presence of demand uncertainty that cannot be contracted upon in the cartel agreement, firms may be better off limiting their collusive agreement to price only. However, a positive relationship between demand uncertainty and the relative profitability of semicollusion exists only for low levels of demand substitutability. The converse is true for high levels of demand substitutability. Therefore, if demand substitutability is sufficiently high, no level of demand uncertainty will make semicollusion the optimal organizational form. In contrast, semicollusion is guaranteed to be optimal for a sufficiently low level of demand substitutability. The market structure described is motivated by and closely parallels that of shipping cartels. Received September 29, 2000; revised version received December 10, 2001 Published online: November 11, 2002     

A note on cartel stability and endogenous sequencing with tacit collusion

We use the concept of cartel stability defined by d’Aspremont et al. (Can J Econ 16(1):17–25, 1983) to obtain that the sequence of play between the cartel and the fringe affects cartel stability in a quantity-competition setting where firms tacitly collude. We also prove that an endogenous sequence of play between a cartel and a fringe depends on the discount factor. If the discount factor is large enough, the cartel and the fringe simultaneously choose quantities since the stable cartel may contain more firms under simultaneous play than under cartel leadership. This is due to the fact that under simultaneous play cartel firms have incentives to participate in the cartel because otherwise no collusion is possible.      

Make a guess: a robust mechanism for King Solomon’s dilemma

We introduce endogenous fees for participating in second-price auction which we use for a two-stage mechanism to solve King Solomon’s dilemma. They are positive for all agents. They are nonetheless shown to maintain the agents’ incentives for truthful bidding and guarantee participation by the highest-value agent. This feature of the endogenous fees is powerful enough for the efficient outcome to uniquely result from one round elimination of weakly dominated strategies, followed by at most four rounds of iterative elimination of strictly dominated stage-strategies. We provide an extension to cases with n agents and k identical prizes. We thank Gary Charness, Harrison Cheng, Jeffrey Ely, Rod Garratt, Mamoru Kaneko, Xiao Luo, Albert Ma, and Steven Morris for helpful discussions. We also thank an anonymous referee for comments that have helped to improve the paper.     

Unique Implementation of the Full Surplus Extraction Outcome in Auctions with Correlated Types

In auctions with correlated types it is possible to design mechanisms such that full surplus extraction can be obtained as the outcome of an equilibrium in which agents use (weakly) dominant strategies. However, it is not assured that the outcome is unique. We present an example in which no mechanism can yield the full surplus extraction outcome as the unique Bayesian equilibrium outcome. Next we show that in the standard auction model the multiplicity problem can be fully resolved using sequential mechanisms, i.e., we show that it is possible to obtain the full surplus extraction outcome as the unique perfect Bayesian equilibrium outcome.Journal of Economic LiteratureClassification Numbers: D44; D70.     

On efficiency of the English auction

We study efficiency properties of the irrevocable exit English auction in a setting with interdependent values. Maskin (1992) [1] shows that the pairwise single-crossing condition is sufficient for efficiency of the English auction with two bidders and suggests that it is also a necessary condition. This paper clarifies and extends Maskin?s results to the case of N bidders. We introduce the generalized single-crossing condition—a fairly intuitive extension of the pairwise single-crossing condition—and prove that it is essentially a necessary and sufficient condition for the existence of an efficient equilibrium of the N-bidder English auction.     

An Optimal Auction for Complements

This paper considers the optimal selling mechanism for complementary items. When buyers are perfectly symmetric, the optimal procedure is to bundle the items and run a standard auction. In general, however, bundling the items is not necessarily desirable, and the standard auctions do not maximize revenue. Moreover, the optimal auction allocation may not be socially efficient since the auction must discriminate against bidders who have strong incentives to misrepresent their true preferences.Journal of Economic LiteratureClassification Number: D44.     

Auction mechanisms and the measurement of WTP and WTA

We evaluate the impact of three auction mechanisms — the Becker–DeGroot–Marschak mechanism, the second-price auction, and the random nth-price auction — in the measurement of willingness to pay (WTP) and willingness to accept (WTA) measures of value. Our results show that initial bidding in trial 1 in each auction does not contradict the endowment effect; but that, if it is the endowment effect that governs people’s initial bidding behavior, it can be eliminated with repetitions of a second-price or random nth-price auction; and if the thesis is that the effect should persist across auctions and across trials is right, our results suggest that there is no fundamental endowment effect.     

Vickrey auctions with reserve pricing

Summary. We generalize the Vickrey auction to allow for reserve pricing in a multi-unit auction with interdependent values. In the Vickrey auction with reserve pricing, the seller determines the quantity to be made available as a function of the bidders' reports of private information, and then efficiently allocates this quantity among the bidders. Truthful bidding is a dominant strategy with private values and an ex post equilibrium with interdependent values. If the auction is followed by resale, then truthful bidding remains an equilibrium in the auction-plus-resale game. In settings with perfect resale, the Vickrey auction with reserve pricing maximizes seller revenues.Received: 31 December 2002, Revised: 5 May 2003, JEL Classification Numbers: D44, C78, D82.Correspondence to: Lawrence M. AusubelThe authors gratefully acknowledge the generous support of National Science Foundation Grants SES-97-31025, SES-01-12906 and IIS-02-05489. We appreciate valuable comments from Ilya Segal. Special thanks go to Mordecai Kurz, who served as Larry's dissertation advisor and who introduced both authors to the economics profession back at IMSSS at Stanford. Congratulations and best wishes are extended to Mordecai and his family on the happy occasion of the publication of Assets, Beliefs, and Equilibria in Economic Dynamics: Essays in Honor of Mordecai Kurz, in which this article also appears.     

Optimality and Robustness of the English Auction

In Milgrom and Weber's (1982, Econometrica50, 1089–1122) “general symmetric model,” under a few additional regularity conditions, the English auction maximizes the seller's expected profit within the class of all posterior-implementable trading procedures and fails to do so among all interim incentive-compatible procedures in which “losers do not pay.” These results suggest that appropriate notions of robustness and simplicity which imply the optimality of the English auction for a risk-neutral seller must impose “bargaining-like” features on the set of feasible trading mechanisms. Journal of Economic Literature Classification Numbers: D44, D82.