The Core and the Equal Division Core in a Three-person Unstructured Bargaining Experiment: The Weakest Coalition is Ignored

Cooperative game theory addresses two problems: coalition formation and payoff distribution. We hypothesize that the existence of the core, which is a fundamental concept in cooperative game theory, affects coalition formation, and we examine this hypothesis through a laboratory experiment. In the experiment, three subjects in a group bargain with each other on both the coalition formation and the payoff distribution simultaneously. The bargaining protocol is unstructured, i.e., similar to a real bargaining situation. As a result, we obtain the following findings. First, the existence of a core strongly induces the formation of the grand coalition. Second, resulting allocations are frequently in the core when it exists and are at least in the equal division core, which is an extension of the core. Finally, resulting allocations that are outside of the equal division core mostly arise due to ignorance of domination via coalition BC, which is the lowest-value two-person coalition.