The scope of auctions in the presence of downstream interactions and information externalities

We scrutinize the scope of auctions for firm acquisitions in the presence of downstream interactions and information externalities. We show that no mechanism exists that allows an investor to acquire a low-cost firm under incomplete information: a separating auction implies adverse selection and relies substantially on commitment to allocation and transfer rules. A pooling auction serves as a commitment device against ex-post opportunistic behavior and alleviates adverse selection. It can earn the investor a higher expected payoff than a separating auction, even when consistency is required as to qualify for a sequential equilibrium.     

Dissolving a partnership (un)fairly

Summary. In an incomplete information, common values setting with risk-neutral agents, we consider mechanisms for allocating the assets of a dissolving partnership where the mechanism designer has no information about the distribution of signals of the agents. We find that the divide and choose mechanism systematically favors the chooser and hence fails on the grounds of fairness. We also examine the fairness properties of the winning and losing bid auctions and show that they systematically favor winning (resp. losing) bidder in ex post allocation of surplus. Finally, we show that a binding arbitration mechanism implements fair allocations.Received: 17 May 2002, Revised: 5 June 2003, JEL Classification Numbers: D39, D44I thank an anonymous referee for extremely helpful suggestions. I also gratefully acknowledge the support of the National Science Foundation and the Hoover Institution.     

Reclaim-proof allocation of indivisible objects

We study desirability axioms imposed on allocations in indivisible object allocation problems. The existing axioms in the literature are various conditions of robustness to blocking coalitions with respect to agentsʼ ex ante (individual rationality and group rationality) and ex post (Pareto efficiency) endowments. We introduce a stringent axiom that encompasses and strengthens the existing ones. An allocation is reclaim-proof if it is robust to blocking coalitions with respect to any conceivable interim endowments of agents. This is an appealing property in dynamic settings, where the assignments prescribed by an allocation to be implemented need to be made in multiple rounds rather than all in one shot. We show that an allocation is reclaim-proof if and only if it is induced by a YRMH–IGYT mechanism (introduced by Abdulkadiroğlu and Sönmez, 1999) and if and only if it is a competitive allocation.     

Matching through position auctions

Using a mechanism design framework, we characterize how a profit-maximizing intermediary can design matching markets when each agent is privately informed about his quality as a partner. Sufficient conditions are provided that ensure a version of positive assortative matching (what we call truncated positive assortative matching) maximizes profits. Under these conditions, all-pay position auctions always implement the profit-maximizing allocation. Winners-pay position auctions, however, only do so in sufficiently large markets.     

Second chance offers versus sequential auctions: theory and behavior

Second chance offers in online marketplaces involve a seller conducting an auction for a single object and then using information from the auction to offer a losing bidder a take-it-or-leave-it price for another unit. We theoretically and experimentally investigate this practice and compare it to two sequential auctions. We show that the equilibrium bidding strategy in the second chance offer mechanism only exists in mixed strategies, and we observe that this mechanism generates more profit for the auctioneer than two sequential auctions. We also observe virtually no rejections of profitable offers in the ultimatum bargaining stage.      

Matching mechanisms and matching quality: Evidence from a top university in China

We compare competing college admission matching mechanisms that differ in preference submission timing (pre-exam, post-exam but pre-score, or post-score) and in matching procedure (Boston (BOS) and serial dictatorship (SD) matching). Pre-exam submission asks students to submit college preferences before entrance exam scores are known, whereas post-score (post-exam) submission removes (reduces) score uncertainties. Theoretical analyses show that although mechanisms with post-score submission or SD matching are ex-post fair and efficient, they are not so ex-ante. Instead, the mechanism with pre-exam submission and BOS matching can be more fair and efficient ex-ante. These hypotheses are supported by empirical test on data from a top school at a top-ranked Chinese university with identification based on temporal and provincial changes. We find that although students admitted under the pre-exam BOS mechanism have lower college entrance exam scores than students admitted through other mechanisms on average, they exhibit similar or even better college academic performance.     

Auctions of Heterogeneous Objects

Simultaneous sealed bid auctions of heterogeneous objects are analyzed. Each bidder's reservation value for an object depends upon the other objects he obtains. Bidders' reservation values are common knowledge. In simultaneous first-price auctions, the set of Walrasian equilibrium allocations contains the set of pure strategy Nash equilibrium allocations which in turn contains the set of strict Walrasian equilibrium allocations. Hence, pure strategy Nash equilibria (when they exist) are efficient. Mixed strategy Nash equilibria may be inefficient. In simultaneous second-price auctions, any efficient allocation can be implemented as a pure strategy Nash equilibrium outcome if a Walrasian equilibrium exists.Journal of Economic LiteratureClassification Numbers: D44, D51.     

Coalitional Strategy-Proofness in Economies with Single-Dipped Preferences and the Assignment of an Indivisible Object

We study two allocation models. In the first model, we consider the problem of allocating an infinitely divisible commodity among agents with single-dipped preferences. In the second model, a degenerate case of the first one, we study the allocation of an indivisible object to a group of agents. Our main result is the characterization of the class of Pareto optimal and coalitionally strategy-proof allocation rules. Alternatively, this class of rules, which largely consists of serially dictatorial components, can be characterized by Pareto optimality, strategy-proofness, and weak non-bossiness (in terms of welfare). Furthermore, we study properties of fairness such as anonymity and no-envy. Journal of Economic Literature Classification Numbers: D63, D71.     

Asymptotic Revenue Equivalence in Auctions

We study the revenue in auctions of a single object when the number of bidders becomes large. We show that all sequences of auctions belonging to a class of mechanisms have limiting expected revenue equal to the expected best-use value of the object. An important special case that is covered is common value auctions, but more generally not even affiliation of values is assumed. This provides an asymptotic revenue equivalence result for settings beyond that of private values. Journal of Economic Literature Classification Numbers: D44, C72.     

Tax enforcement,tax compliance and tax morale in transition economies: A theoretical model

The focus of this paper is the analysis of the relationship between tax enforcement, tax compliance and tax morale within countries characterised by rapid introduction of market institutions and slow evolution of political regimes, such as transition economies. The paper investigates a coordination game in which the government is ex-ante committed to tax enforcement and can observe the proportion of tax-compliant agents in the economy. In turn, two groups of agents (third-party reporting and self-reported income) are keen to evade taxes unlawfully but have limited information on how many others evade taxes; their tax morale is therefore an endogenous function of agents' perception on tax compliance. The model predicts that the lower the quality of political institutions and the weaker tax morale, the less tax compliance can be achieved. The third-party reporting group will also be bearing higher tax burden than the self-reported income group. The model entails that having political institutions of good quality is not a sufficient condition to conduce to tax enforcement or tax compliance. Due to the endogenous role of tax morale, the government could be pushed ex-post towards poor or no tax enforcement. If good political institutions are not accompanied by good information about the enforcement of tax collection, there is scope for co-existence of poor tax enforcement, low tax compliance and weak tax morale. As such, this model well describes the tax evasion behaviour observed since the outset of transition from planned to market economy.     

Mixed bundling auctions

We study multi-object auctions where agents have private and additive valuations for heterogeneous objects. We focus on the revenue properties of a class of dominant strategy mechanisms where a weight is assigned to each partition of objects. The weights influence the probability with which partitions are chosen in the mechanism. This class contains efficient auctions, pure bundling auctions, mixed bundling auctions, auctions with reserve prices and auctions with pre-packaged bundles. For any number of objects and bidders, both the pure bundling auction and separate, efficient auctions for the single objects are revenue-inferior to an auction that involves mixed bundling.     

Worst-case optimal redistribution of VCG payments in multi-unit auctions

For allocation problems with one or more items, the well-known Vickrey–Clarke–Groves (VCG) mechanism (aka Clarke mechanism, Generalized Vickrey Auction) is efficient, strategy-proof, individually rational, and does not incur a deficit. However, it is not (strongly) budget balanced: generally, the agents' payments will sum to more than 0. We study mechanisms that redistribute some of the VCG payments back to the agents, while maintaining the desirable properties of the VCG mechanism. Our objective is to come as close to budget balance as possible in the worst case. For auctions with multiple indistinguishable units in which marginal values are nonincreasing, we derive a mechanism that is optimal in this sense. We also derive an optimal mechanism for the case where we drop the non-deficit requirement. Finally, we show that if marginal values are not required to be nonincreasing, then the original VCG mechanism is worst-case optimal.     

On The Allocative Effects of Rent Seeking

We consider the effects of rent-seeking activities on resource allocation. Before rent-seeking activities take place, there are prior probabilities that an object will be given to one of several agents. The posterior probability depends on prior probabilities and the expenses incurred by all agents. In the case of two agents who equally value the object, prior and posterior probabilities coincide, and thus rent seeking has no effect on resource allocation. If there are two agents with different valuations of the object or we have more than two agents, rent seeking matters and posterior probabilities reflect the valuations of the agents.     

Optimal shill bidding in the VCG mechanism

This paper studies shill bidding in the Vickrey?CClarke?CGroves (VCG) mechanism applied to combinatorial auctions. Shill bidding is a strategy whereby a single decision-maker enters the auction under the guise of multiple identities (Yokoo et?al. Games Econ Behav, 46?pp. 174?C188, 2004). I formulate the problem of optimal shill bidding for a bidder who knows the aggregate bid of her opponents. A key to the analysis is a subproblem??the cost minimization problem (CMP)??which searches for the cheapest way to win a given package using shills. An analysis of the CMP leads to several fundamental results about shill bidding: (i) I provide an exact characterization of the aggregate bids b such that some bidder would have an incentive to shill bid against b in terms of a new property Submodularity at the Top; (ii) the problem of optimally sponsoring shills is equivalent to the winner determination problem (for single minded bidders)??the problem of finding an efficient allocation in a combinatorial auction; (iii) shill bidding can occur in equilibrium; and (iv) the problem of shill bidding has an inverse, namely the collusive problem that a coalition of bidders may have an incentive to merge (even after competition among coalition members has been suppressed). I show that only when valuations are additive can the incentives to shill and merge simultaneously disappear.     

Revealing information in auctions: the allocation effect

When there are two bidders, releasing independent information in an English auction with private values makes the seller worse off. However, this is no longer true with more bidders: when there is enough competition, revelation benefits the auctioneer. In three examples the dividing case is shown to be three bidders. This allocation effect applies to other standard auctions and parallels the bundling decision in a multi-unit auction. I would like to thank Jeremy Bulow, Willie Fuchs, Paul Klemperer, Rob McMillan, Phil Reny, Jeff Zwiebel and especially Andy Skrzypacz. I also grateful to two referees and an Associate Editor for a number of helpful comments.     

Almost common values auctions revisited

In almost common-value auctions one bidder (the advantaged bidder) has a valuation advantage over all other (regular) bidders. It is well known that in second-price auctions with two bidders, even a slight private-value advantage can have an explosive effect on auction outcomes as the advantaged bidder wins all the time and auction revenue is substantially lower than in a pure second-price common-value auction. We explore the robustness of these results to the addition of more regular bidders in second-price auctions, and the extent to which these results generalize to ascending-price English auctions in an effort to provide insight into when and why one ought to be concerned about such slight asymmetries.     

We can't disagree forever

Under the assumption of common priors, if the information partitions of two agents are finite, then simply by communicating back and forth and revising their posteriors the two agents will converge to a common equilibrium posterior, even though they may base their posteriors on quite different information. Furthermore, given any integer, n, one can construct an example in which the revision process not only takes n steps to converge, but no evident revision occurs—for (n?1) steps both agents repeat the same conflicting posteriors—until the last step, when the two agents decide to agree. Common knowledge of each other's posterior does not necessarily lead agents to the posterior they would have agreed upon had information been directly exchanged. On the other hand, the examples that are characterized by a discrepancy between the direct and indirect communication equilibrium, are rare: with probability 1, the revision process constructed here leads the two agents in one step to the direct communication equilibrium.     

Selling options

Contracts often take the form of options: oil fields can be abandoned, planning permission may go unused, and acquired firms can be liquidated. We consider a seller who auctions a dynamic option among N agents. After the auction, the economy evolves and the winning bidder chooses both if and when to execute the option. The revenue-maximising auction consists of an up-front bid and a contingent fee, where the latter is chosen in a Pigouvian manner, so the winning agent's choice of exercise time maximises the seller's revenue. This contingent payment is time- and state-invariant, so the seller does not have to observe post-auction information in order to implement the optimal auction. The revenue-maximising mechanism induces a dynamic distortion: the option is exercised later than under the comparable welfare-maximising mechanism.     

The role of optimal threats in auction design

This paper studies revenue-maximizing auctions when buyers' outside options depend on their private information and are endogenously chosen by the seller. We show that the revenue-maximizing assignment of the object can depend crucially on the outside options that the seller can choose as threats. Depending on the shape of outside options, sometimes an optimal mechanism allocates the object in an ex-post efficient way, and, other times, buyers obtain the object more often than is efficient.     

Rates of information aggregation in common value auctions

We study the rates at which transaction prices aggregate information in common value auctions under the different information structures in Wilson (Rev. Econ. Stud. 44 (1977) 511) and Pesendorfer and Swinkels (Econometrica 65 (1997) 1247). We consider uniform-price auctions in which k identical objects of unknown value are auctioned to n bidders, where both n and k are allowed to diverge to infinity, and k/n converges to a number in [0,1). The Wilson assumptions lead to information aggregation at a rate proportional to , but the price aggregates information at a rate proportional to in the PS setting. We also consider English auctions, and investigate whether the extra information revealed in equilibrium improves convergence rates in these auctions.