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 cq > 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)- 0; 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