The Influence of structural relationships on coalition formation in four‐person apex games

Abstract

AbstractEight quartets of subjects each played eight different versions of a 4‐person apex game twice, in a computer‐controlled coalition formation experiment. The eight games were cast into a 2 × 2 factorial mold in which (i) the central apex player was either weak or strong in terms of the outcomes available to Apex coalitions, and (ii) the outcomes to players not in coalitions varied, such that the outside opportunities of the Base players were not necessarily equal.The data were analyzed from the point of view of coalition frequencies, payoff allocations, and a bargaining process examination of the computer‐recorded protocols. The H competitive bargaining set is shown to be a first‐order predictor of payoff allocations, but differences not accountable by that model are also manifest. The manipulation of the strength of the Apex player affected coalition frequencies such that strong Apex players were in more coalitions than weak Apex players. Somewhat contrary to expectation, no effect for differential outside opportunities of Base players were shown. The analysis of the bargaining protocols revealed structural and psychological factors not considered in present mathematical models that must be incorporated into any model aspiring to provide a coherent description of coalition formation processes.