Feasible mechanisms in economies with type-dependent endowments.

We propose two classes of allocation games for N.T.U. and T.U. exchange economies in which initial endowments and preferences depend on the agents’ private information. In both models, agents make non-verifiable claims about their types and effective deposits of consumption goods, which are redistributed by the planner. In a W-allocation game, the agents can withhold part of their endowment, namely consume whatever they do not deposit. In a D-allocation game, the agents can just destroypart of their endowment. W- and D- incentive compatible (I.C.) direct allocation mechanisms ask every agent to reveal his type and to make a deposit consistent with his reported type. The revelation principle holds in full generality for D-I.C. mechanisms but some care is needed for W-I.C. mechanisms. We further investigate the properties of both classes of mechanisms under common assumptions like non-exclusive information and/or constant aggregate endowment. In T.U. economies, W-I.C. and D-I.C. mechanisms are ex ante equivalent.Théorie des jeux;

On the Failure of Core Convergence in Economies with Asymmetric Information

In interim economies with asymmetric information, we show that the coarse core of Wilson (1978) does not converge to price equilibrium allocations as the economy is replicated. This failure of core convergence is a basic consequence of asymmetric information and extends to any reasonable notion of either (interim) core or price equilibrium.core, price equilibrium, asymmetric information, interim economies, sunspot economies.

On the Failure of Core Convergence in Economies with Asymmetric Information

In interim economies with asymmetric information, we show a robust failure of the core convergence theorem. We begin by showing that the coarse core of Wilson (1978) does not converge to any set of price equilibrium allocations considered in the literature. To prove our main point we construct a simple example of a replicated sunspot economy with strictly convex and monotonic preferences. We also show that the coarse core may not satisfy the equal treatment property. Moreover, coarse core allocations satisfying the equal treatment property may not converge to price equilibrium allocations. The result applies to any notion of price equilibrium (including rational expectations equilibria, Radner equilibria, sunspot equilibria) in which fully informed consumers receive a consumption plan maximizing ex-post utility over the ex-post budget set. The non-convergence result holds for several different notions of the interim core proposed in the literature, including the fine core (Wilson (1978)), the private core (Yannelis (1991)), the core in the pooling case (Ichiishi and Idzik (1996), Goenka and Shell (1997)), the incentive compatible core (Vohra (1999)), the coarse+ core (Lee and Volij (forthcoming)), the core with endogenous communication (Volij (forthcoming)). This failure of core convergence is a basic consequence of asymmetric information, which at the interim stage, imposes important restrictions on coalition formation. (Informational constraints may rule out many coalitions of types of consumers that would be present in the standard Debreu and Scarf (1963) complete information framework.) In particular, our negative results do not rely on the lack of `informational smallness' of agents (at least in the sense in which this term has recently been formalized in McLean and Postlewaite (1999)).

Allocative and Informational Externalities in Auctions and Related Mechanisms

We study the effects of allocative and informational externalities in (multi-object) auctions and related mechanisms. Such externalities naturally arise in models that embed auctions in larger economic contexts. In particular, they appear when there is downstream interaction among bidders after the auction has closed. The endogeneity of valuations is the main driving force behind many new, specific phenomena with allocative externalities: even in complete information settings, traditional auction formats need not be efficient, and they may give rise to multiple equilibria and strategic non-participation. But, in the absence of informational externalities, welfare maximization can be achieved by Vickrey-Clarke- Groves mechanisms. Welfare-maximizing Bayes-Nash implementation is, however, impossible in multi-object settings with informational externalities, unless the allocation problem is separable across objects (e.g. there are no allocative externalities nor complementarities) or signals are one-dimensional. Moreover, implementation of any choice function via ex-post equilibrium is generically impossible with informational externalities and multidimensional types. A theory of information constraints with multidimensional signals is rather complex, but indispensable for our study

Preliminary Results for Cooperative Extensions of the Bayesian Game

The descriptive theory of cooperative game with incomplete information developed to date is surveyed. The theory has the potential to provide game-theoretical foundations of economic analysis of the free societies in which organizations (coalitions) as corporations institute a non-market resource allocation mechanism while using the market resource allocation mechanism at the same time. The present-day corporations are interdependent, so the required game theory needs to model an environment in which the feasibility and implications of coordinated strategy choice within a coalition are influenced by the outsiders of strategy choice. The first part of the paper provides the key ingredients. After formulating the basic one-shot model, which synthesizes Harsanyi's Bayesian game and Aumann and Peleg's non-side-payment game (NTU game), and illustrating economic examples, two required conditions on an endogenously determined strategy are discussed: measurability with respect to an information structure, and Bayesian incentive compatibility. Several descriptive solution concepts that have been proposed to date are discussed. The second part addresses six issues studied in the literature: First, the existence of the descriptive solutions in the general setup. Second, explanation of information revelation, that is, a process through which private information turns into public information. Third, definitions of efficiency. Fourth, comparisons of several core concepts. Fifth, the existence results specific only to the Bayesian pure exchange economy, and revival of the core convergence theorem within the framework of the Bayesian pure exchange economy. Sixth, another view on coalition formation, specifically analyses of situations in which coalitional membership is anonymous.

Core-stable Rings in Auctions with Independent Private Values

We propose a semi-cooperative game theoretic approach to check whether a given coalition is stable in a Bayesian game with independent private values. The ex ante expected utilities of coalitions, at an incentive compatible (noncooperative) coalitional equilibrium, describe a (cooperative) partition form game. A coalition is core-stable if the core of a suitable characteristic function, derived from the partition form game, is not empty. As an application, we study collusion in auctions in which the bidders’ final utility possibly depends on the winner’s identity. We show that such direct externalities offer a possible explanation for cartels’ structures (not) observed in practice.auctions, Bayesian game, collusion, core, partition function game

Herd behavior, the "Penguin effect", and the suppression of informational diffusion: An analysis of informational externalities and payoff interdependency

Technology;Information;Econometric Models;Group Behaviour