Logic meets cognition:Empirical reasoning in games

This paper presents a first attempt to bridge the gap between logical and cognitive treatments of strategic reasoning in games. The focus of the paper is backward induction, a principle which is purported to follow from common knowledge of rationality by Zermelo's theorem. There have been extensive formal debates about the merits of principle of backward induction among game theorists and logicians. Experimental economists and psychologists have shown that human subjects, perhaps due to their bounded resources, do not always follow the backward induction strategy, leading to unexpected outcomes. Recently, based on an eye-tracker study, it has turned out that even human subjects who produce the outwardly correct 'backward induction answer' use a different internal reasoning strategy to achieve it. This paper presents a formal language to represent different strategies on a finer-grained level than was possible before. The language and its semantics may lead to precisely distinguishing different cognitive reasoning strategies, that can then be tested on the basis of computational cognitive models and experiments with human subjects.