Nonsymmetry and Core Size in N-Person Sidepayment Games

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Abstract
This article presents a procedure for indexing n-person cooperative games in terms of degree of nonsymmetry. This ordinal-level index is limited to sidepayment games, but applies generally to games of three or more players. To validate the index, a laboratory experiment was conducted with four-person games differing in degree of nonsymmetry and in core size. The results show that, while core size had no significant effects, the players' payoffs varied significantly as a function of nonsymmetry. Strong players received increasingly more and weak players received increasingly less as nonsymmetry increased. Tests for goodness of fit of several prominent solution concepts show that, across experimental treatments, the Shapley value predicts better than other solutions. Shapley is followed in order by the disruption nucleolus, the nucleolus, and finally the equality solution. These tests also show that all of the theories decline in predictive accuracy as the degree of nonsymmetry increases. Reasons for this trend are discussed in terms of predictive patterns and payoff variances.