This contrasts with the models of Falk and Fischbacher (1999) and Fehr and Schmidt (1999) because the payoff differences between the third party and the other players matter in these models. Thus, the third party may well punish the defector because the defector earns more than the third party. However, both models have difficulties in explaining the fact that mutual defection is also punished, because the payoff vector in this case is (25, 25, 40) before the punishment decision of C. Since Player C is better off than both A and B, Player C should never punish in this situation, but in fact, 20.8% of the third parties punished, albeit at a rather low level. The model of Levine (1998) is again consistent with the existence of third-party punishment of defectors because defection may be taken as a signal that the defector is a greedy subject.

XREF: Connects to the broader third-party punishment literature in behavioral economics and game theory, where models of Fehr-Schmidt and Falk-Fischbacher assume payoff comparisons drive punishment.

Ernst Fehr, Third-Party Punishment and …, loc. 66