Collective bargaining in a shrinking group game: The role of information and communication

Abstract

Majority decisions often resolve situations that involve strategic considerations of several individuals. Although these individuals often have identical voting power, their strategic position may be different. We utilize the pirate game in which a pre-existing minimum winning coalition emerges from the subgame perfect Nash equilibrium. This opens the possibility of investigating how equilibrium information about being pivotal and communication in different group constellations affect the size of proposals of the different players. Our results provide evidence that equilibrium information considerably increases the pivotal players' position at the expense of the non-pivotal players. This effect goes far beyond mere coordination of a pivotal triplet if this group has no information about the equilibrium. Communication leads more towards an equal distribution amongst the communication participants in both the subgroup and the large group. Whole group communication, directly following communication within informed subgroups, diminishes the pivotal players’ advantage, although not completely.