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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 cl > a and if it was tempting, player 1 gets ch > cl. 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 [ap + ch(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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