of the temptation, but more costly if the temptation is high. Thus, if the temptation is

of the temptation, but more costly if the temptation is high. Thus, if the temptation is low, player 1 gets a > 0 if she cooperates and q > a if she defects. If the temptation is high, she gets a if she cooperates and cp, > c if she defects. We assume that cooperation benefits the other player, which we refer to as player 2. We assume, for simplicity, that player 2 gets 6 > 0 if 1 cooperates and d < 0 if 1 defects, and that these payoffs to player 2 are the same regardless of 1’s temptation. For now, we also assume that d < p/(1 —p)-; that is, defection is sufficiently harmful to player 2 that player 2 prefers to avoid the interaction if player 1 only cooperates some of the time. Finally, we model player 2’s trust in player 1. We model this by giving player 2 the choice of whether to continue the interaction with player 1. If player 2 continues the interaction, then with probability w, all previous steps are repeated, potentially indefinitely. That is, the temptation to defect is randomly chosen again, player 1 chooses whether to look at it, and so on. With probability 1 — w, the game ends. The parameter w can be interpreted as the likelihood of a future interaction or the player’s discounting of future payoffs. Crucially, we assume that player 2 observes both of player 1’s choices: not only whether 1 cooperated, but also whether 1 first looked. Our model, therefore, applies to situations where player 1’s looking is somewhat observable, for example, if player 1 can gain additional information about the costs of defection by asking player 2 questions, or if player 1 can take time to ponder the decision and player 2 can observe player 1’s reaction time. We assume that players maximize their expected payoffs. Note that since we assumed a > 0 and 6 > 0, both players benefit from a cooperative interaction. In the envelope game, a strategy for player 1 dictates whether she will look and whether she will cooperate, as a function of whether she has looked and cooperated in the past, and as a function of the temptation if she has just looked. For example, one relatively simple strategy for player 1 is to look and cooperate whenever the temptation is low. HOUSE_OVERSIGHT_026524