Correlated equilibria and communication in games.

Analyse bayésienne; Théorie des jeux; Information privée;

The ex ante incentive compatible core of an exchange economy with and without indivisibilities.

Le coeur ex ante incitatif d'une économie d'échange en information incomplète est le coeur, au sens de la théorie des jeux coopératifs standard, d'une fonction caractéristique qui rend compte du fait que les coalitions allouent les biens grâce à des mécanismes aléatoires incitatifs. Nous passons d'abord en revue quelques résultats dans le cas de biens parfaitement divisibles. Des exemples montrent alors que coeur ex ante incitatif peut être vide, même si les fonctions d'utilité sont quasi-linéaires. Si, en plus de la quasi-linéarité, on formule des hypothèses supplémentaires, telles que les valeurs privées et indépendantes, on peut établir la non-vacuité du coeur en construisant des mécanismes incitatifs efficaces ex post, suivant la méthode de d'Aspremont et Gérard-Varet. Nous introduisons également de l' information incomplète dans les économies avec biens divisibles de Shapley et Scarf et nous démontrons que le coeur ex ante incitatif est toujours non-vide dans ce cadre.The ex ante incentive compatible core of an exchange economy with private information is the (standard) core of a characteristic function which expresses the fact that coalitions allocate goods by means of random incentive compatible mechanisms. We first survey some results in the case of perfectly divisible goods. Examples then show that the ex ante incentive compatible core can be empty, even if utility functions are quasi-linear. If, in addition to quasi-linearity, further assumptions are made (like independent private values), the non-emptiness of the core follows nevertheless from d'Aspremont and Gérard-Varet's construction of incentive compatible, ex post efficient mechanisms. We also introduce a private information version of Shapley and Scarf's economies with indivisible goods, and prove that the ex ante incentive compatible core is always non-empty in this framework.Information incomplète; Mécanisme incitatif; Biens indivisibles;

Digital system provides superregulation of nanosecond amplifier-discriminator circuit

Feedback system employing a digital logic comparator to detect and correct amplifier drift provides stable gain characteristics for nanosecond amplifiers used in counting applications. Additional anticoincidence logic enables application of the regulation circuit to the amplifier and discriminator while they are mounted in an operable circuit

Communication in Bayesian games: Overview of work on implementing mediators in game theory.

game theory; Bayesian games;

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;

The Ex Ante Incentive Compatible Core in Exchange Economies with and without Indivisibilities

The ex ante incentive compatible core of an exchange economy with private information is the (standard) core of a socially designed characteristic function, which expresses the fact that coalitions allocate goods by means of random incentive compatible mechanisms. We first survey some results in the case of perfectly divisible goods. Examples then show that the ex ante incentive compatible core can be empty, even if utility functions are quasi-linear. If, in addition to quasi-linearity, further assumptions are made (like independent private values), the non-emptiness of the core follows nevertheless from d’Aspremont and Gérard-Varet’s construction of incentive compatible, ex post efficient mechanisms. We also introduce a private information version of Shapley and Scarf’s economies with indivisible goods, and prove that the ex ante incentive compatible core is always non-empty in this framework.core, incentive compatible mechanism, indivisible goods, private information

Cooperative Games with Incomplete Information: Some Open Problems

This is a brief survey describing some of the recent progress and open problems in the area of cooperative games with incomplete information. We discuss exchange economies, cooperative Bayesian games with orthogonal coalitions, and issues of cooperation in non-cooperative Bayesian games.#

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

Core-stable rings in second price auctions with common values.

In a commonvalueauction in which the information partitions of the bidders are connected, all rings are core-stable. More precisely, the ex ante expected utilities of rings, at the (noncooperative) sophisticated equilibrium proposed by Einy et al. [Einy, E., Haimanko, O., Orzach, R., Sela, A., 2002. Dominance solvability of second-pricesauctions with differential information. Journal of Mathematical Economics 37, 247–258], describe a cooperative games in characteristic function form, in spite of the underlying strategic externalities. A ring is core-stable if the core of this characteristic function is not empty. Furthermore, every ring can implement its sophisticated equilibrium strategy by means of an incentive compatible mechanism. An example shows that, if the bidders’ information partitions are not connected, rings may no longer be core-stable.Characteristic function; Partition form game; Core; Collusion; Bayesian game; Auctions;