The core and the equal division core in a three-person unstructured bargaining experiment

Cooperative game theory addresses two main problems: coalition formation and payoff distribution. We hypothesize that the existence and size of the core, a central concept in cooperative game theory, influence the formation of the grand coalition, and we test this in a laboratory experiment. In each group, three subjects simultaneously engage in unstructured bargaining over both coalition formation and payoff distribution, mimicking real-world negotiation. Our results highlight four key findings. First, a nonempty core strongly facilitates the formation of the grand coalition. Second, the availability of a chat window increases the likelihood of forming the grand coalition and reduces inequality in the resulting allocations. Third, resulting allocations are often in the core when it exists, and otherwise fall within the equal division core, an extension of the core. Fourth, the resulting allocations reflect the subjects’ theoretical bargaining power: players with higher bargaining power tend to receive larger shares. Finally, allocations outside the equal division core arise mainly because subjects overlook domination via coalition BC, the two-person coalition with the lowest value.