Knowledge of the Game, Relative Rationality, and Backwards Induction without Counterfactuals. Working Paper No. 25, Leipzig Graduate School of Management

ABSTRACT. We analyse epistemic conditions for the backwards induction play in games of perfect information. Unlike most previous literature on the subject, we explicitly pay attention to players’ knowledge of the game, avoid counterfactuals, and use the syntactic approach of the epistemic logic KT. Moreover, taking doxastic possibility to be the dual of knowledge, we introduce a concept of relative rationality in the sense of rational choice from the moves one considers possible. The main result says that the backwards induction play is implied by sufficiently high order mutual knowledge of (1) the structure of the game, (2) relative rationality, and (3) conditional doxastic possibility of all moves which belong to the backwards induction profile. For a certain class of games, we also show that replacing (3) by conditional possibility of some other profile S, does not imply play according to S. Moreover, we show that our sufficient condition for the BI play is weaker than the one of Aumann (1995)