Seminar

Optimal Reputation Management with a Control and Information Theoretic Approach

Nuh Aygun Dalkiran (Bilkent University)

April 7, 2015, 11:00–12:30

Toulouse

Room MS 001

Economic Theory Seminar

Abstract

We analyze reputation games where a strategic long-run player acts in a repeated game against a collection of short-lived (myopic) Bayesian players: An infinite horizon discounted payoff optimal strategy for the long-run player is obtained through a control theoretic approach. A dynamic programming formulation is obtained for the computation of optimal strategies for the long-run player; the existence of an optimal stationary strategy and, under further assumptions, the continuity of the equilibrium payoffs in the perturbations are established. The undiscounted average payoff problem and the arbitrarily patient long-run player settings are also considered, where $\epsilon$-optimality of stationary strategies in the undiscounted problem has been established for any $\epsilon > 0$ and an Abelian Theorem is used to recover an upper payoff bound for the arbitrarily patient long-run player where this upper bound is identified with a Stackelberg equilibrium. Furthermore, by using measure concentration techniques a lower payoff bound on reputation is obtained. Our findings provide alternative interpretations of existing results in the field, but also provide generalizations in view of new results on the structure of equilibrium strategies, continuity results in the prior probabilities, and upper and lower bounds on the value of reputations.