Surplus extraction with rich type spaces

We characterize revenue maximizing mechanisms in auction settings with ‘rich’ type spaces, where bidders obtain information from sources other than their own valuation. By considering a relaxed problem, we provide an upper bound on revenue extraction that explicitly builds on the richness of the information structure. We provide a condition under which this upper bound is achieved and describe an optimal mechanism. Under this condition, we also show that the optimal revenue can be achieved through dominant strategy implementation.     

Pigouvian pricing and stochastic evolutionary implementation

We study the implementation of efficient behavior in settings with externalities. A planner would like to ensure that a group of agents make socially optimal choices, but he only has limited information about the agents’ preferences, and can only distinguish individual agents through the actions they choose. We describe the agents’ behavior using a stochastic evolutionary model, assuming that their choice probabilities are given by the logit choice rule. We prove that there is a simple price scheme with the following property: regardless of the realization of preferences, a group of agents subjected to the price scheme will spend the vast majority of time in the long run behaving efficiently. The price scheme defines a game that may possess multiple equilibria, but we are able to obtain a unique and efficient selection from this set because of the stochastic nature of the agents’ choice rule. We conclude by comparing the performance of our price scheme with that of VCG mechanisms.     

Subgame perfect implementation: A full characterization

Moore and Repullo [Subgame perfect implementation, Econometrica 56 (1988) 1191-1220], and Abreu and Sen [Subgame perfect implementation: a necessary and almost sufficient condition, J. Econ. Theory 50 (1990) 285-299] introduce distinct necessary and sufficient conditions for SPE implementation, when the number of players is at least three. This paper closes the gap between the conditions—a complete characterization of the SPE implementable choice rules is provided. The characterization consists of α^*, which strengthens α of Abreu-Sen by adding it a restricted veto-power condition, and the unanimity condition. Under strict preferences α^* is equal to α.     

Robust monopoly pricing

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version, the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution. We characterize the pricing policies under two distinct decision criteria with multiple priors: (i) maximin utility and (ii) minimax regret. The equilibrium price under either criterion is lower then in the absence of uncertainty. The concern for robustness leads the seller to concede a larger information rent to all buyers with values below the optimal price without uncertainty.     

Market games with differential information and infinite dimensional commodity spaces: The core

Summary We provide an alternative proof of the existence of core allocations in exchange economies with differential information and infinite dimensional commodity spaces. We also identify a critical feature of information sharing rules that ensures nonemptiness of the core. In essence, the only condition we require on the sharing rules is that profitable insider trading be prohibited. In the absence of insider trading, balancedness is guaranteed and core nonemptiness follows.I thank Dan Arce, Erik Balder, Myrna Wooders, and Nicholas Yannelis for helpful comments. This paper is a greatly revised version of my paper entitled. A Variational Problem Arising in Market Games with Differential Information, written in August of 1991.     

Operators for the adjudication of conflicting claims

We consider the problem of allocating some amount of an infinitely divisible and homogeneous resource among agents having claims on this resource that cannot be jointly honored. A “rule” associates with each such problem a feasible division. Our goal is to uncover the structure of the space of rules. For that purpose, we study “operators” on the space, that is, mappings that associate to each rule another one. Duality, claims truncation, and attribution of minimal rights are the operators we consider. We first establish a number of results linking them. Then, we determine which properties of rules are preserved under each of these operators, and which are not.     

A new necessary condition for implementation in iteratively undominated strategies

We uncover a new necessary condition for implementation in iteratively undominated strategies by mechanisms that satisfy the “best element property” where for each agent, there exists a strategy profile that gives him the highest payoff in the mechanism. This class includes finite and regular mechanisms. We conclude that either the quasilinearity-like assumptions of available sufficiency results cannot be completely dispensed with or some mechanisms that do not satisfy the best element property must be employed. We term the condition “restricted deception-proofness.” It requires that, in environments with identical preferences, the social choice function be immune to all deceptions, making it then stronger than incentive compatibility. In some environments the conditions for (exact or approximate) implementation by mechanisms satisfying the best element property are more restrictive than previously thought.     

Equilibrium selection in global games with strategic complementarities

We study games with strategic complementarities, arbitrary numbers of players and actions, and slightly noisy payoff signals. We prove limit uniqueness: as the signal noise vanishes, the game has a unique strategy profile that survives iterative dominance. This generalizes a result of Carlsson and van Damme (Econometrica 61 (1993) 989-1018) for two-player, two-action games. The surviving profile, however, may depend on fine details of the structure of the noise. We provide sufficient conditions on payoffs for there to be noise-independent selection.     

ROBUST RATIONALIZABILITY UNDER ALMOST COMMON CERTAINTY OF PAYOFFS

An action is robustly rationalizable if it is rationalizable for every type who has almost common certainty of payoffs. We illustrate by means of an example that an action may not be robustly rationalizable even if it is weakly dominant, and argue that robust rationalizability is a very stringent refinement of rationalizability. Nonetheless, we show that every strictly rationalizable action is robustly rationalizable. We also investigate how permissive robust rationalizability becomes if we require that players be fully certain of their own payoffs.     

Robustness of equilibria in anonymous local games

This paper studies the robustness of symmetric equilibria in anonymous local games to perturbations of prior beliefs. Two priors are strategically close on a class of games if players receive similar expected payoffs in equilibrium under the priors, for any game in that class. I show that if the structure of payoff interdependencies is sparse in a well-defined sense, the conditions for strategic proximity in anonymous local games are strictly weaker than the conditions for general Bayesian games of Kajii and Morris (1998) [11] when attention is restricted to symmetric equilibria. Hence, by exploiting the properties of anonymous local games, it is possible to obtain stronger robustness results for this class.     

Limited observability as a constraint in contract design

Limited observability is the assumption that economic agents can only observe a finite amount of information. Given this constraint, contracts among agents are necessarily finite and incomplete in comparison to the ideal complete contract that we model as infinite in detail. We consider the extent that finite contracts can approximate a complete contract. The objectives of the paper are: (i) to identify properties of agents’ preferences that determine whether or not finiteness of contracts causes significant inefficiency; (ii) to evaluate the performance of finite contracts against the ideal optimal contract in a bilateral bargaining model.     

Monopolistic Screening with Boundedly Rational Consumers*

In this paper, I revisit the monopolistic screening problem with two types assuming that consumers are boundedly rational. Bounded rationality implies that the revelation principle does not apply and the choice of the selling mechanism entails a loss of generality. I show that if the monopolist restricts attention to the mechanisms that offer menus of two choices, the profits are lower than in the case of fully rational consumers by the term of order ln λ/λ, where λ is the degree of rationality of the consumers. The monopolist, however, can approximate the profits earned when consumers are fully rational by using a more elaborate message game.     

On the strategic impact of an event under non-common priors

This paper studies the impact of a small probability event on strategic behavior in incomplete information games with non-common priors. It is shown that the global impact of a small probability event (i.e., its propensity to affect strategic behavior at all states in the state space) has an upper bound that is an increasing function of a measure of discrepancy from the common prior assumption. In particular, its global impact can be arbitrarily large under non-common priors, but is bounded from above under common priors. These results quantify the different implications common prior and non-common prior models have on the (infinite) hierarchies of beliefs.     

Competitive experimentation with private information: The survivor's curse

We study a winner-take-all R&D race between two firms that are privately informed about the arrival rate of an invention. Over time, each firm only observes whether the opponent left the race or not. The equilibrium displays a strong herding effect, that we call a ‘survivor's curse.’ Unlike in the case of symmetric information, the two firms may quit the race (nearly) simultaneously even when their costs and benefits for research differ significantly.     

Generalized potentials and robust sets of equilibria

This paper introduces generalized potential functions of complete information games and studies the robustness of sets of equilibria to incomplete information. A set of equilibria of a complete information game is robust if every incomplete information game where payoffs are almost always given by the complete information game has an equilibrium which generates behavior close to some equilibrium in the set. This paper provides sufficient conditions for the robustness of sets of equilibria in terms of argmax sets of generalized potential functions. These sufficient conditions unify and generalize existing sufficient conditions. Our generalization of potential games is useful in other game theoretic problems where potential methods have been applied.     

Theories of behavior in principal-agent relationships with hidden action

In a laboratory experiment, we investigate behavior in a principal-agent situation with moral hazard. We evaluate the predictive success of two theories. One is the standard agency theory, which assumes that the agent will accept any contract offer that satisfies his participation constraint, typically requiring zero expected utility. The other is the “fair-offer” theory suggested by Keser and Willinger [2000. Principals’ principles when agents’ actions are hidden. International Journal of Industrial Organization 18 (1), 163-185], which requires that the principal provide full insurance against losses to the agent and leave him a share of at most 50% of the generated surplus. The treatment variable of our experiment is the cost of effort. As effort costs increase, expected net surplus of a contract decreases. We observe that fair-offer theory generally predicts observed contract offers better than standard agency theory. However, the predictive success of the fair-offer theory decreases, while the one of standard agency theory increases with decreasing expected net surplus.     

Non-existence of monotone equilibria in games with correlated signals

Participation in economic games such as auctions is typically costly, which means that players (potential bidders) must consider whether to participate. Such decisions may be no less crucial than how to bid, and yet the literature has been mostly concerned with bidding, assuming an exogenously given number of bidders; see Krishna [Auction Theory, Academic Press, New York, 2002]. Landsberger and Tsirelson [Correlated signals against monotone equilibria, preprint SSRN 222308, Social Science Research Network Electronic Library, May 2000. Available online: http://papers.ssrn.com/abstract=222308] have shown that fundamental results established in symmetric auction theory with correlated signals, such as the existence of a monotone equilibrium, may not hold if participation decisions are part of equilibrium. The major goal of this paper is to illustrate and explain this result that may be considered counter intuitive given the emphasis placed on monotone equilibria in the auction literature.     

Characterising equilibrium selection in global games with strategic complementarities

Global games are widely used to predict behaviour in games with strategic complementarities and multiple equilibria. We establish two results on the global game selection. First, we show that, for any supermodular complete information game, the global game selection is independent of the payoff functions chosen for the game?s global game embedding. Second, we give a simple sufficient criterion to derive the selection and establish noise independence in many-action games by decomposing them into games with smaller action sets, to which we may often apply simple criteria. We also report in which small games noise independence may be established by counting the number of players or actions.     

Efficient collusion in repeated auctions with communication

This paper studies collusion in repeated auctions when bidders communicate prior to each stage auction. For independent and correlated private signals and general interdependent values, the paper identifies conditions under which an equilibrium collusion scheme is fully efficient in the sense that the bidders’ payoff is close to what they get when the object is allocated to the highest valuation bidder at the reserve price in every period.     

Bid rotation and collusion in repeated auctions

This paper studies bidder collusion with communication in repeated auctions when no side transfer is possible. It presents a simple dynamic bid rotation scheme which coordinates bids based on communication history and enables intertemporal transfer of bidders’ payoffs. The paper derives a sufficient condition for such a dynamic scheme to be an equilibrium and characterizes the equilibrium payoffs in a general environment with affiliated signals and private or interdependent values. With IPV, it is shown that this dynamic scheme yields a strictly higher payoff to the bidders than any static collusion scheme which coordinates bids based only on the current reported signals.