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Solving Imperfect-Information Games

In imperfect-information games, for every subgame, players’ equilibrium strategies are coupled with the strategies outside the subgame. Thus it is assumed that each subgame can not be solved in isolation and strategies of the entire game should be considered as a whole. In the literature, one way to compute these equilibrium strategies is to first find an approximate solution of the entire game and then improve it in individual subgames. In this paper, we show that each subgame can indeed be solved in isolation by providing an additional variable with each history, which is the public belief on unknown variables. Using this approach, we present an algorithm to compute equilibrium strategies of a zero-sum sequential imperfect information game.