Sharing Information Without Regret in Managed Stochastic Games

Abstract: This paper considers information sharing in a multi-player repeated game. Every round, each player observes a subset of components of a random vector and then takes a control action. The utility earned by each player depends on the full random vector and on the actions of others. An example is a game where different rewards are placed over multiple locations, each player only knows the rewards in a subset of the locations, and players compete to collect the rewards. Sharing information can help others, but can also increase competition for desirable locations. Standard Nash equilibrium and correlated equilibrium concepts are inadequate in this scenario. Instead, this paper develops an algorithm where, every round, all players pass their information and intended actions to a game manager. The manager provides suggested actions for each player that, if taken, maximize a concave function of average utilities subject to the constraint that each player gets an average utility no worse than it would get without sharing. The algorithm acts online using information given at each round and does not require a specific model of random events or player actions. Thus, the analytical results of this paper apply in non-ergodic situations with any sequence of actions taken by human players.