In the assurance (meeting-place) game in this chapter, the payoffs were meant to describe the value of something material that the players gained in the various outcomes; they could be prizes given...

In the assurance (meeting-place) game in this chapter, the payoffs were meant to describe the value of something material that the players gained in the various outcomes; they could be prizes given for a successful meeting, for example. Then other individual persons in the population might observe the expected payoffs (fitness) of the two types, see which was higher, and gradually imitate the fitter strategy. Thus, the proportions of the two types in the population would change. But we can make a more biological interpretation. Suppose the column players are always female and the row players always male. When two of these players meet successfully, they pair off, and their children are of the same type as the parents. Therefore, the types would proliferate or die off as a result of successful or unsuccessful meetings. The formal mathematics of this new version of the game makes it a “two-species game” (although the biology of it does not). Thus, the proportion of S-type females in the population—call this proportion x—need not equal the proportion of S-type males—call this proportion y.

(a) Examine the dynamics of x and y by using methods similar to those used in the chapter for the battle-of-the-sexes game.

(b) Find the stable outcome or outcomes of this dynamic process.