Optimal Behavioral Strategies In 0-Sum Games with Almost Perfect Information

This paper provides the general construetion of the optimal strategies in a special class of zero sum games with incomplete information, those in which the players move sequentially. It is shown that at any point of the game tree, a player's optimal behavioral strategy may be derived from a state variable involving two components: the first one keeps track of the information he revealed, the second one keeps track of the (vector) payoff he should secure over his opponent's possible position. This construction gives new insights on earlier results obtained in the context of sequential repeated games. Several examples are discussed in detail.