Risky cooperation: two-person Public Goods Game
After completing the competition stage, participants played a one-shot, two-player public goods game (PGG). This provides the simplest environment to assess how participants behaved toward their opponents within the context of risky cooperation. At the start of the PGG, participants were informed of their endowment (100 tokens with an exchange value of 10 tokens per￥1), that of the player with whom they were matched, and whether or not this person had been allocated their endowment. First, participants were asked to indicate their own willingness to cooperate as well as their predictions about their opponents’ willingness to cooperate on a 9-point rating scale (1 = not at all to 9 = very much respectively). Given that there is some evidence showing differences in self-other decision makingParticipants had to decide how many tokens they wished to contribute to the public good and predict how many their opponents would contribute. The order of these predictions was also counterbalanced across participants to prevent order effects. The number of tokens that had been donated to the public good was then multiplied by a factor that was known to participants before they contributed. Multiplying contributions by a factor larger than the number of players can guarantee a positive return from participants’ contributions, which means that allocations to the public good can be purely based on their self-interest. This produced a final amount that was then evenly divided between the players irrespective of who had contributed the most. As such, personal earnings comprised the sum of tokens that participants did not contribute to the public good plus their share of the payment from the public good. We applied three α: 1.4, 2, and 3 to the amounts contributed. In this sense, our modified PGG allowed participants to make decisions about cooperation with their opponents when their cooperative behavior involved either a high risk of incurring personal costs, no risk of incurring personal costs, or mutual gains. Specifically, when α = 1.4, participants run a high risk of personal costs. For example, a contribution of 40 tokens, when multiplied by 1.4, would result in an 
overall amount of 56. Thus, if the opponent decides to contribute nothing, the participant will receive less than their initial contribution (56/2 = 28). When α = 2, there is no risk but gains are not guaranteed. For example, a contribution of 40 tokens, when multiplied by 2, would only bring about an overall amount of 80. Thus, if the opponent decides to contribute nothing, the participant will receive the same as their initial contribution (80/2 = 40). In this situation, the opponent would benefit from the participant’s contribution. When α = 3 however, risk is again 0 but gain this time is guaranteed, regardless of whether the opponent decides to contribute. For example, a contribution of 40 tokens, when multiplied by 3, would result in an overall amount of 120. Thus, even though the opponent decides to contribute nothing, both the participant and the opponent will still receive more than the participant’s initial contribution (120/2 = 60) (Fig. 