over time under the assumption that the rate of reproduction within each population

over time under the assumption that the rate of reproduction within each population is proportional to the fitness relative to that type’s other strategies. Since replicator dynamics cannot be solved in closed form, they must analyzed using computer simulations seeded with randomly chosen strategy frequencies. This method also requires restricting the analysis to a few strategies. Therefore, we run our replicator analysis only on the restricted set of strategies represented in figure 2. While this set of strategies is restricted, it includes the potentially destabilizing mutants discussed above. To investigate the frequencies in which different equilibria emerge, we randomly seed the strategy frequencies many times and record the frequency of each strategy after the population has stabilized. Many mixtures of strategies are behaviorally consistent with CWOL, for example, if a large enough fraction of player 2s exit when player 1s look then no player 1s will look, even if this fraction is less than 1. Thus, we classify population frequencies as being behaviorally equivalent to ALLD, CWL, and CWOL (see appendix for details). We plot the frequencies of each of these for different values of a in figure 3 (see appendix for analogous figures for other parameters). As can be seen, CWOL emerges often when it is a Nash Equilibrium. Next, we identify the conditions under which people will be most likely to avoid looking and detect looking amongst others. For this, we interpret the conditions under which CWOL is the only cooperative equilibrium, because, as we show in the appendix, when one allows for mutations, the CWOL equilibrium no longer emerges in dynamic simulations when both CWOL and CWL are equilibria. Recall that CWL is a Nash equilibrium if and only if -+, > cy. This equilibrium condition has a natural interpretation: in order to sustain CWL, the long term gains to player 1 from the ongoing relationship must suffice for player 1 to cooperate even when player 1 knows the temptation is high in the current period. Contrast this with the condition that determines if CWOL is an equilibrium: HOUSE_OVERSIGHT_026527