Zero-Sum Games with “Almost” Perfect Information

The present paper generalizes the concept of perfect information to games in which the players, while moving sequentially, remain uncertain about the actual payoff of the game because of an initial chance move. It is proved that the value of such games with “almost” perfect information can still be computed using backward induction in the game tree. The optimal behavioral strategies obtained by a dynamic procedure may, however, require randomization. A typical illustration of such games is poker.