Public information in Markov games

In a Markov game, players engage in a sequence of games determined by a Markov process. In this setting, this paper investigates the impact of varying the informativeness of public information, as defined by Blackwell 1951 and 1953, pertaining to the games that will be played in future periods. In brief, when a curvature condition on payoffs is satisfied, the finding is that, for any fixed discount factor, the set of strongly symmetric subgame perfect equilibrium payoffs of a Markov game with more informative signals is contained in this set of equilibrium payoffs if the Markov game is played with any less informative signals. The second result shows that larger equilibrium payoffs are possible with less informative signals when the curvature condition fails, but only for some discount factors. The third result strengthens the curvature condition, but generalizes the first result to all subgame perfect equilibrium payoffs. Finally, a collusion application is presented to illustrate the curvature condition.