Effects of grand coalition payoffs on coalition formation in three-person games

This study investigates the effects of the values of one part of a living system, a group, on the system as a whole and the relationship among the group members. Eight quarters of male undergraduate subjects participated in a computer-controlled experiment designed to study the effects of the relative magnitude of payoffs to the three-person grand coalition on bargaining and coalition formation behavior in three-person games. The experimental design employed five sets of quota values and four different grand coalition values for each set of quotas. Various conceptual systems, mathematical models from game theory, were tested and the bargaining process itself was examined. The results are analyzed in terms of the frequency with which different coalition types were formed, the disbursement of the payoffs, the progress of the bargaining process from initial phases to the final phases, and the nature of the bargaining process. Results show that as the value of that grand coalition increases, the frequency of the grand coalition also increases. The kernel and bargaining set M1(i), are supported as predictors of the final outcomes, while the Shapley value model is rejected as inadequate. Several significant effects due to the value of the grand coalition are observed and some insights into the bargaining process are obtained.