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HOUSE_OVERSIGHT_026526

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attending to looking. In the appendix, we formalize this intuition by showing that this equilibrium is subgame perfect, a solution concept used to rule out these kinds of concerns in settings where there is a high degree of rationality [15]. We might wonder whether CWOL will emerge in a population of players who are not rational, but are evolving or learning their strategies. There are two reasons to suspect it will not emerge. First, CWOL may be susceptible to the invasion of mutants. In particular, the concern is that a player 2 mutant might arise that does not attend to whether player 1 looks, rendering looking irrelevant. This mutant’s fitness is no higher or lower than the incumbent strategy, so may grow by drift. Subsequently, a player 1 mutant which looks and defects when the temptation is high would have a fitness advantage and proliferate. While the player 2 mutant would then start dying off since it would now have lower fitness than the incumbent, it is not clear that it would do so fast enough for the player 1 mutant to also die off, returning to the CWOL equilibrium. Second, CWOL may be stable but have such a small basin of attraction that it will never emerge. In particular, there are three other equilibria to consider, which can be seen in figure 2. The first is comprised of the strategy pair where player 1 always defects, and player 2 always exits (which we refer to as the ALLD equilibrium). It is a Nash Equilibrium for all parameter values. The second is the strategy pair where player 2 exits if player 1 defects, and player 1 cooperates with or without looking (we refer to this as the CWL equilibrium). It is a Nash equilibrium when ;*, = 2. In fact, there are many more Nash Equilibria, where the population mixes between different strategies. Consequently, we employ computer simulations of the replicator dynamic to explore the evolutionary dynamics of the envelope game. The replicator dynamic is the standard model for evolutionary dynamics [16, 17,

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