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Knowledge-Based Rational Decisions

We outline a mathematical model of rational decision-making based on standard game-theoretical assumptions: 1) rationality yields a payoff maximization given the player’s knowledge; 2) the standard logic of knowledge for Game Theory is the modal logic S5. Within this model, each game has a solution and rational players know which moves to make at each node. We demonstrate that uncertainty in games of perfect information results exclusively from players’ different perceptions of the game. In strictly competitive perfect information games, any level of players’ knowledge leads to the backward induction solution which coincides with the maximin solution. The same result holds for the well-known centipede game: its standard ‘backward induction solution’ does not require any mutual knowledge of rationality.