Varieties of strategic reasoning in games

A crucial assumption underlying any game-theoretic analysis is that there is common knowledge that all the players are rational. Rationality here is understood in the decision-theoretic sense: The players’ choices are optimal according to some choice rule (such as maximizing subjective expected utility). Recent work in epistemic game theory has focused on developing sophisticated mathematical models to study the implications of assuming that all the players are rational and this is commonly known (or commonly believed). 1 However, if common knowledge of rationality is to have an “explanatory” role in the analysis of a game-theoretic situation, then it is not enough to simply assume that it has obtained in an informational context of a game. It is also important to describe how the players were able to arrive at this crucial state of information. 2 There is now a growing body of literature that analyzes games in terms of the “process of deliberation” that leads the players to select their component of a rational outcome (see [17] for a discussion). There is a second reason why it is important to develop formal models of the players’ process of deliberation in game situations. A number of researchers have questioned the usefulness of models that make explicit assumptions about the players’ higher-order beliefs in game situations. In the end, we are interested only in what (rational) players are going to do. This, in turn, depends only on what the players believe the other players are going to do. A player’s belief about what her opponents are thinking is relevant only because they shape the players’ first-order beliefs about what her opponents are going to do. Kadane and Larkey explain the issue nicely: