Introduction and examples

Many strategic problems of interest take place in contexts where, unlike what has been implicitly assumed so far, players do not have complete information on the underlying features of the situation. Often, this happens because, even though players accurately know their individual payoffs, they have only imprecise information on the payoffs earned by others for some possible paths of play. And then, of course, any uncertainty about their opponents' payoffs typically must have an important bearing on how players analyze the strategic situation and make their respective choices. To obtain a preliminary glimpse of the important considerations involved, let us first consider some illustrative (yet informal) examples.

Recall the game we labeled battle of the sexes, first introduced in Section 1.1 (Table 1.2). As in that game, suppose the boy and the girl confront (simultaneously) the decision of whether to go shopping or attend the basketball game. The payoffs for the boy are as postulated before. Concerning the girl, however, now suppose that her payoffs may a priori be of two different sorts: she may either be a “shopping fan,” or a “basketball fan.” If she is the first, she always prefers to go shopping, no matter what the boy does; if she is the second (a basketball fan), her best option is always to go to the basketball game, again independently of what the boy decides.