Figure Legends
Figure 1: The Envelope Game
We model non-strategic cooperative behavior using what we call the envelope game. (a) Column 1: The game begins when the temptation to defect is randomly chosen, as indi- cated by a notice randomly being placed in the envelope. The temptation to defect is low with probability p and high with probability 1— p. Column 2: Then, player 1 chooses whether to look (open the envelope) or not. Column 3: Player 1 then chooses whether to cooperate or defect. Player 1 may only condition her action on the realized temptation determined in column 1 if she looked. Each time player 1 cooperates, then, regardless of whether player 1 looked, player 1 gets a > 0 and player 2 gets b > 0. Each time player 1 defects, her payoffs depend on whether defection was tempting. If it was not tempting, player 1 gets q¢ > a and if it was tempting, player 1 gets c, > q. In either case, each time player 1 defects, player 2 gets d < 0. Column 4: Player 2, having observed both of player 1’s choices, chooses whether to continue or exit. If player 2 continues, with probability w,
all previous steps are repeated, potentially indefinitely. Figure 2: Payoffs for a Restricted Set of Strategies in the Envelope Game
This table presents the payoffs for the restricted set of strategies used for the replicator analysis. Player 1’s strategies are presented in separate rows, and player 2’s strategies are presented in columns. The payoffs presented in the intersection of a given row and column are those that the players receive if they play the corresponding strategies. For example, consider what happens if player 1 looks and cooperates only if the temptation is low (penultimate row) and player 2 repeats continues when player 1 cooperates (middle
column). Then, player 1’s expected payoff is jap + c¢;,(1—p)][1— pw] (the first entry in
the corresponding cell) and player 2’s is [bp + d(1 — p)][1 — pw] (the second entry in the
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