Condorcet Jury Theorem: An example in which informative voting is rational but leads to inefficient information aggregation

Recent research on the Condorcet Jury Theorem has proven that informative voting (that is, voting according to one’s signal) is not necessarily rational. With two alternatives, rational voting typically leads to the election of the correct alternative, in spite of the fact that not all voters vote informatively. We prove that with three alternatives, there are cases in which informative voting is rational and yet leads to the election of a wrong alternative.     

Asymmetric information, strategic behavior, and discrimination in the labor market

Summary  The neoclassical model of labor market discrimination assumes the presence of either prejudiced preferences, biased assessments of worker productivity, or monopsony power. We show that when market agents control asymmetric information, strategic behavior can induce discriminatory hiring practices even when these market features are absent. Moreover, strategic interaction many distort public policies to the point of harming the segments of the work force they were designed to support. Received: January 3, 1996 revised version April 29, 1996     

Information transmission in coalitional voting games

A core allocation of a complete information economy can be characterized as one that would not be unanimously rejected in favor of another feasible alternative by any coalition. We use this test of coalitional voting in an incomplete information environment to formalize a notion of resilience. Since information transmission is implicit in the Bayesian equilibria of such voting games, this approach makes it possible to derive core concepts in which the transmission of information among members of a coalition is endogenous. Our results lend support to the credible core of Dutta and Vohra [Incomplete information, credibility and the core, Math. Soc. Sci. 50 (2005) 148-165] and the core proposed by Myerson [Virtual utility and the core for games with incomplete information, Mimeo, University of Chicago, 2005] as two that can be justified in terms of coalitional voting.     

The type-agent core for exchange economies with asymmetric information

The type-agent core is a new solution concept for exchange economies with asymmetric information. It coincides with the set of subgame-perfect equilibrium outcomes of a simple competitive screening game. Uninformed intermediaries help the agents to cooperate in an attempt to make some profit. The paper extends the work of Perez-Castrillo [Cooperative outcomes through non-cooperative games, Games Econ. Behav. 7 (1994) 428-440] to exchange economies with non-transferable utility and asymmetric information. The type-agent core is a subset of Wilson's coarse core [Wilson, Information, efficiency, and the core of an economy, Econometrica 46 (1978) 807-816]. It is never empty, even though it may be a strict subset of Wilson's fine core. In addition, it converges towards the set of constrained market equilibria as the economy is replicated.     

THE SECOND‐PRICE AUCTION SOLVES KING SOLOMON'S DILEMMA*

The planner wants to give k identical, indivisible objects to the top k valuation agents at zero costs. Each agent knows her own valuation of the object and whether it is among the top k. Modify the (k+ 1)st‐price sealed‐bid auction by introducing a small participation fee and the option not to participate in it. This simple mechanism implements the desired outcome in iteratively undominated strategies. Moreover, no pair of agents can profitably deviate from the equilibrium by coordinating their strategies or bribing each other.     

Group play in games and the role of consent in network formation

We study games played between groups of players, where a given group decides which strategy it will play through a vote by its members. When groups consist of two voting players, our games can also be interpreted as network-formation games. In experiments on Stag Hunt games, we find a stark contrast between how groups and individuals play, with payoffs playing a primary role in equilibrium selection when individuals play, but the structure of the voting rule playing the primary role when groups play. We develop a new solution concept, robust-belief equilibrium, which explains the data that we observe. We provide results showing that this solution concept has application beyond the particular games in our experiments.     

Do bad risks know it? Experimental evidence on optimism and adverse selection

Subjects who overestimate their performance in experimental tasks unrelated to travel are less willing to insure against failing in the task and also less inclined to buy travel insurance. This suggests intrinsic optimism influences insurance demand and diminishes adverse selection.     

Serial cost sharing of excludable public goods: general cost functions

Summary. A group of individuals meet to share the cost and determine output allocations of a partial-excludable public good. We demonstrate that, for general cost functions and preferences that satisfy the Spence-Mirlees sorting condition, the serial cost-sharing formula (Moulin, 1994) has remarkable incentive properties. First, a direct economic mechanism that uses the serial formula is coalition strategy-proof, envy-free and satisfies the stand-alone property. Second, the serial mechanism involves partial exclusion, which is important for the reduction of the free-rider problem. Received: June 10, 1996; revised version; February 11, 1997     

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.     

Persuasion,binary choice,and the costs of dishonesty

We study the strategic interaction between a decision maker who needs to take a binary decision but is uncertain about relevant facts and an informed expert who can send a message to the decision maker but has a preference over the decision. We show that the probability that the expert can persuade the decision maker to take the expert’s preferred decision is a hump-shaped function of his costs of sending dishonest messages.     

Minimal stable sets in tournaments

We propose a systematic methodology for defining tournament solutions as extensions of maximality. The central concepts of this methodology are maximal qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy of tournament solutions, encompassing the top cycle, the uncovered set, the Banks set, the minimal covering set, and the tournament equilibrium set. Moreover, the hierarchy includes a new tournament solution, the minimal extending set, which is conjectured to refine both the minimal covering set and the Banks set.     

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.     

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.     

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.     

An efficient solution to the informed principal problem

In this paper I study mechanism design by an informed principal. I show that generically this problem has an ex-post efficient solution. In the equilibrium mechanism, the informed principal appropriates all expected social surplus, with each type of her getting all expected social surplus conditional on that type. This outcome is supported as a perfect sequential equilibrium of the informed principal game when the joint probability distribution from which the agents’ types are drawn satisfies two conditions: the well-known condition of Cremer and McLean and Identifiability condition introduced by Kosenok and Severinov [Individually rational, budget-balanced mechanisms and allocation of surplus, J. Econ. Theory (2002), forthcoming]. Conversely, these conditions are necessary for an ex-post efficient outcome to be attainable in an equilibrium of the informed principal game. Under these conditions only our equilibrium outcome constitutes a neutral optimum, i.e. cannot be eliminated by any reasonable concept of blocking [R. Myerson, Mechanism design by an informed principal, Econometrica 51 (1983) 1767-1797]. Identifiability and Cremer-McLean conditions are generic when there are at least three agents, and none of them has more types than the number of type profiles of the other agents.     

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.