Deductive Reasoning in Extensive Games*

In many economic contexts decision makers interact and take actions that extend through time. A bargaining party makes an offer, which is observed by the adversary, and accepted, rejected or followed by a counter-offer. Firms competing in markets choose prices, levels of advertisement, or investments with the intent of thereby influencing the future behaviour of competitors. One could add many examples. The standard economic model for analysing such situations is that of an extensive game. This paper is concerned with the following question: What happens in an extensive game if players reason deductively by trying to figure out one another’s moves? We have in Asheim and Dufwenberg (2002) (AD) proposed a model for deductive reasoning leading to the concept of ‘fully permissible sets’, which can be applied to many strategic situations. In this paper we argue that the model is appropriate for analysing extensive games and we apply it to several such games.