In many two-player games, players that invest in punishment finish with lower payoffs than those who abstain from punishing. These results question the effectiveness of punishment at promoting cooperation, especially when retaliation is possible. It has been suggested that these findings may stem from the unrealistic assumption that all players are equal in terms of power. However, a previous empirical study which incorporated power asymmetries into an iterated prisoner's dilemma (IPD) game failed to show that power asymmetries stabilize cooperation when punishment is possible. Instead, players cooperated in response to their partner cooperating, and punishment did not yield any additional increase in tendency to cooperate. Nevertheless, this previous study only allowed an all-or-nothing–rather than a variable–cooperation investment. It is possible that power asymmetries increase the effectiveness of punishment from strong players only when players are able to vary their investment in cooperation. We tested this hypothesis using a modified IPD game which allowed players to vary their investment in cooperation in response to being punished. As in the previous study, punishment from strong players did not increase cooperation under any circumstances. Thus, in two-player games with symmetric strategy sets, punishment does not appear to increase cooperation.
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