Similarly, a strategy for player 2 dictates whether he will continue or exit as a function

Similarly, a strategy for player 2 dictates whether he will continue or exit as a function of everything player 1 has done in the past. One relatively simple strategy for player 2 is to continue so long as player 1 has cooperated. If both players play according to this pair of strategies, each time the temptation is low, player 1 cooperates and gets a, player 2 gets b, and the game continues with probability w until the first time the temptation is high. Then, player 1 defects and gets c, and player 2 gets d. Some straightforward calculations yield the players’ expected payoffs: player 1’s is [ap + c,(1 — p)] / [1 — pw] and player 2’s is [bp + d(1 — p)| / [1 — pw]. Because a strategy specifies players’ moves in every period and the game’s length is undetermined, infinitely many possible strategies exist. We are primarily interested in the seven strategies represented in Figure 2, which shows the expected payoff for each player for each strategy pair of interest. Of particular interest is the strategy pair designated in the top left corner of figure 2), in which player 2 discriminates between cooperators who look and those who do not look, and player 1 cooperates without looking (CWOL). The following simple argument demonstrates that this strategy pair is a Nash Equilibrium (which means no player has an incentive to unilaterally deviate) whenever ~*~ > qp+cp(1—p). This condition has a natural interpretation: player 1’s expected temptation from defection is less than the gains from an ongoing cooperative interaction. Thus, player 1 would lose from deviating, for example by looking, because this would end the lucrative ongoing relationship, reducing a Le player 1’s payoff from an expected to 0. Player 2 would also lose from deviating, by choosing to exit, because when player 1 is always cooperating, she expects oo from the relationship, and exiting yields 0. One potential concern with this equilibrium is that, since player 2 is not worse off by not attending to looking, he might not do so. This turns out to not be the case. The intuition is that if there is even a small probability player 1 looks, player 2 is better off HOUSE_OVERSIGHT_026525