Game Theory normally assumes enough knowledge to avoid uncertainty completely or to deal with its probabilistically. We outline a mathematical model of rational decision-making under uncertainty which is based on standard game-theoretical postulates:

• rationality yields a payoff maximization given the player’s knowledge;
• the logic of knowledge for Game Theory is the modal logic S5,

and does not rely on any probabilistic assumptions. Within this model, each game has a solution regardless to the epistemic states of rational players.

We show 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.

Reading:

S. Artemov. Knowledge-Based Rational Decisions. Technical Report TR-2009011 CUNY Ph.D. Program in Computer Science, 2009 http://tr.cs.gc.cuny.edu/tr/techreport.php?id=382