The controlled biased coin problem
Résumé
We study the maxmin value of a zero-sum repeated game where player 1 is restricted to pure strategies but privately observes the realizations of some random variables. This kind of problem was introduced by Gossner and Vieille [GV02] in the case where player 1 observes i.i.d. random variables. The paper solves the case where the law of the random variable (the coin) depends on player 1's action. We also discuss the general case where the law of the coin is controlled by both players.