Perfect Communication Equilibria in Repeated Games with Imperfect Monitoring.

This paper introduces an equilibrium concept called perfect communication equilibrium for repeated games with imperfect private monitoring. This concept is a refinement of Myerson's [Myerson, R.B., 1982. Optimal coordination mechanisms in generalized principal agent problems, J. Math. Econ. 10, 67–81] communication equilibrium. A communication equilibrium is perfect if it induces a communication equilibrium of the continuation game, after every history of messages of the mediator. We provide a characterization of the set of corresponding equilibrium payoffs and derive a Folk Theorem for discounted repeated games with imperfect private monitoring.Repeated games; Imperfect monitoring; Communication equilibria;

Entropy Bounds on Bayesian Learning.

An observer of a process View the MathML source believes the process is governed by Q whereas the true law is P. We bound the expected average distance between P(xt|x1,…,xt−1) and Q(xt|x1,…,xt−1) for t=1,…,n by a function of the relative entropy between the marginals of P and Q on the n first realizations. We apply this bound to the cost of learning in sequential decision problems and to the merging of Q to P.Bayesian learning; Repeated decision problem; Value of information; Entropy;

Information Design for Strategic Coordination of Autonomous Devices with Non-Aligned Utilities

In this paper, we investigate the coordination of autonomous devices with non-aligned utility functions. Both encoder and decoder are considered as players, that choose the encoding and the decoding in order to maximize their long-run utility functions. The topology of the point-to-point network under investigation, suggests that the decoder implements a strategy, knowing in advance the strategy of the encoder. We characterize the encoding and decoding functions that form an equilibrium, by using empirical coordination. The equilibrium solution is related to an auxiliary game in which both players choose some conditional distributions in order to maximize their expected utilities. This problem is closely related to the literature on "Information Design" in Game Theory. We also characterize the set of posterior distributions that are compatible with a rate-limited channel between the encoder and the decoder. Finally, we provide an example of non-aligned utility functions corresponding to parallel fading multiple access channels.Comment: IEEE Proc. of the Fifty-fourth Annual Allerton Conference Allerton House, UIUC, Illinois, USA September 27 - 30, 201

Mechanism Design and Communication Networks

This paper characterizes the class of communication networks for which, in any environment (utilities and beliefs), every incentive-compatible social choice function is (partially) implementable. Among others, in environments with either common and independent beliefs and private values or a bad outcome, we show that if the communication network is 2-connected, then any incentive-compatible social choice function is implementable. A network is 2-connected if each player is either directly connected to the designer or indirectly connected to the designer through at least two disjoint paths. We couple encryption techniques together with appropriate incentives to secure the transmission of each player’s private information to the designer.Mechanism design; incentives; Bayesian equilibrium; communication networks; encryption; secure transmission; coding

Finitely repeated games with semi-standard monitoring

This paper studies finitely repeated games with semi-standard monitoring played in pure strategies. In these games, each player's action set is endowed with a partition, and the equivalence classes of the actions played are publicly observed. We characterize the limit set of equilibrium payoffs as the duration of the game increases.Finitely repeated games, semi-standard monitoring, folk theorem.

A minority game with bounded recall.

This paper studies a repeated minority game with public signals, symmetric bounded recall, and pure strategies. We investigate both public and private equilibria of the game with fixed recall size. We first show how public equilibria in such a repeated game can be represented as colored subgraphs of a de Bruijn graph. Then we prove that the set of public equilibrium payoffs with bounded recall converges to the set of uniform equilibrium payoffs as the size of the recall increases. We also show that private equilibria behave badly: A private equilibrium payoff with bounded recall need not be a uniform equilibrium payoff.folk theorem; de Bruijn sequence; imperfect monitoring; uniform equilibrium; public equilibrium; private equilibrium;