Stochastic Control Approach to Reputation Games
Abstract
Through a stochastic control theoretic approach, we analyze reputation games where a strategic longlived player acts in a sequential repeated game against a collection of shortlived players. The key assumption in our model is that the information of the shortlived players is nested in that of the longlived player. This nested information structure is obtained through an appropriate monitoring structure. Under this monitoring structure, we show that, given mild assumptions, the set of Perfect Bayesian Equilibrium payoffs coincide with Markov Perfect Equilibrium payoffs, and hence a dynamic programming formulation can be obtained for the computation of equilibrium strategies of the strategic longlived player in the discounted setup. We also consider the undiscounted averagepayoff setup where we obtain an optimal equilibrium strategy of the strategic longlived player under further technical conditions. We then use this optimal strategy in the undiscounted setup as a tool to obtain a tight upper payoff bound for the arbitrarily patient longlived player in the discounted setup. Finally, by using measure concentration techniques, we obtain a refined lower payoff bound on the value of reputation in the discounted setup. We also study the continuity of equilibrium payoffs in the prior beliefs.
 Publication:

arXiv eprints
 Pub Date:
 April 2016
 arXiv:
 arXiv:1604.00299
 Bibcode:
 2016arXiv160400299A
 Keywords:

 Mathematics  Optimization and Control;
 Computer Science  Computer Science and Game Theory
 EPrint:
 To appear in IEEE Transactions on Automatic Control