Coalition formation in characteristic function games: Competitive tests of three theories

Abstract

Two experiments tested the bargaining, minimum resource, and minimum power theories of coalition formation in situations involving different payoffs for some of the winning coalitions (characteristic function games). In the first experiment, a triadic resource distribution was employed and payoffs for the coalitions were specified in such a way that each of the three theories predicted the formation of a different coalition. The coalition predicted by minimum power theory formed the most frequently, and the mean divisions of the payoffs among coalition members were also closest to the predictions of minimum power theory. However, the most frequent coalition was not only the one predicted by minimum power theory, it was also the one having the largest payoff per member. There-fore, a second experiment was conducted, which employed a tetradic resource distribution and specified the coalition payoffs in such a way that (a) each of the theories predicted the formation of a different coalition and (b) none of the predicted coalitions was the one with the largest payoff per member. Although the mean payoff divisions in the coalitions in this experiment were closest to those predicted by bargaining theory, the coalition that formed most frequently was not one of those predicted by any of the theories. Rather, it was the one having the largest payoff per member. None of the three theories is able to account adequately for the results of both experiments. The difficulties that the theories have in dealing with coalition formation in situations in which there are different payoffs for winning are discussed.