Logique dynamique pour le raisonnement stratégique dans les jeux extensifs

This paper continues the dynamic modal logic analysis provided by van Benthem [5] of procedural rationality in games. Specifically we look at extensive games, and use preference logic to provide a closer analysis of backward induction type algorithms. This results in distinguishing two kinds of rationality : decision rationality and preference rationality. To these two kinds of rationality correspond game transformations, for which we give syntactic counterparts in a modal logic. In the final model arrived at through transformations of a nongeneric game, there can be paths which are in no subgame-perfect equilibrium. More generally the nature of solutions that our approach can induce is incompatible with the retrospective nature of the usual concepts of game theory. We end the paper with some remarks on potential uses of such a modal logic analysis to the cases of imperfect information or where rationality is bounded.