Logic & Philosophy of Science Colloquium

The formal representations of games provided by game theory contain information, not only about what happens as a game is played, but also about what would have happened if things had gone differently - about what players would believe and what they would do if the other players had acted differently - and this counterfactual information is important to the explanation and evaluation of what does happen. But counterfactual information remains for the most part implicit in the apparatus that game theory uses to define a game and to model the way it is played; it is reflected� in the specifications of� tree structures, information sets, strategies and conditional probability functions which are naturally interpreted as representing the causal structure of the game and the capacities and behavioral dispositions of the players. My aim in this talk is to make explicit the counterfactual information that is implicit in these specifications by adding to game models a semantics for conditional propositions. Semantic models for conditional logic, based on selection functions, or comparative similarity relations on possible worlds, apply naturally to game models, since the rich structure imposed by the definition of a game provides criteria for the comparative similarity relations on possible worlds that constrain the interpretation of conditional propositions. The application of conditional semantics to game models throws light in two directions: first, it helps to clarify some game theoretic concepts (such a the concept of a strategy) and some complex patterns of strategic reasoning; second, it brings into focus some general features of the problem of interpreting counterfactuals and helps to clarify the relation between counterfactual propositions and dispositional properties