The consistent preferences approach to deductive reasoning in games

The Consistent Preferences Approach to Deductive Reasoning in Games presents, applies, and synthesizes what my co-authors and I have called the 'consistent preferences' approach to deductive reasoning in games. Briefly described, this means that the object of the analysis is the ranking by each player of his own strategies, rather than his choice. The ranking can be required to be consistent (in different senses) with his beliefs about the opponent's ranking of her strategies. This can be contrasted to the usual `rational choice' approach where a player's strategy choice is (in different senses) rational given his beliefs about the opponent's strategy choice. Our approach has turned out to be fruitful for providing epistemic conditions for backward and forward induction, and for defining or characterizing concepts like proper, quasi-perfect and sequential rationalizability. It also facilitates the integration of game theory and epistemic analysis with the underlying decision-theoretic foundation. TOC:Introduction.- Motivating Examples.- Decision-Theoretic Framework.- Belief Operators.- Basic Characterizations.- Relaxing Completeness.- Backward Induction.- Sequentiality.- Quasi-Perfectness.- Properness.- Capturing Forward Induction Through Full Permissibility.- Applying Full Permissibility To Extensive Games.