Mollifier Representation in Non-Constant-Sum Games

This article reports an experimental test that juxtaposes the von Neumann-Morgenstern characteristic function v(S) against the homomollifier function h(S) proposed by Charnes et al. (1978). The test was conducted in the context of 5-person cooperative sidepayment non-constant-sum games with nonempty core. Experimental results show that payoff predictions by various solution concepts (the Shapley value, the nucleolus, the 2-center) computed from the homomollifier are more accurate than predictions by the same solutions computed from the characteristic function. Supplementary analyses of data show that the payoff function x(S) is more closely approximated by the homomollifier h(S) than by the characteristic function v(S). These findings are interpreted as indicating that the homomollifier is more useful than the characteristic function for purposes of predicting payoffs in non-constant-sum games.