Too big to Prevail: Coalition Formation in the Presence of a Superpower

We investigate the effect of players' power on the formation of coalitions to divide a prize when the assumption that coalition formation involves binding agreements on how to split the prize is relaxed. In our experimental setup with one powerful ('strong') player and three standard ('weak') players, we vary the strong player's voting rights as one dimension and manipulate the timing of agreement on the prize division as the other dimension. We predict and find: first, with binding agreement at the coalition formation stage, the resulting allocation is, by and large, in line with the relative power of the players as measured by their Shapley value. Second, when binding agreement on the prize division is not possible at the coalition formation stage, the strong player's likelihood to be part of the winning coalition and her average payoff decrease significantly if she becomes "too strong". Third, communication at the coalition formation stage only weakly mitigates this negative effect of the absence of binding agreements for powerful players.