Bargaining for Coalition Structure Formation

Many multiagent settings require a collection of agents to partition themselves into coalitions. In such cases, the agents may have conflicting preferences over the possible coalition structures that may form. We investigate a noncooperative bargaining game to allow the agents to resolve such conflicts and partition themselves into non-overlapping coalitions. The game has a finite horizon and is played over discrete time periods. The bargaining agenda is defined exogenously. An important element of the game is a parameter 0 ≤ δ ≤ 1 that represents the probability that bargaining ends in a given round. Thus, δ is a measure of the degree of democracy (ranging from democracy for δ = 0, through increasing levels of authoritarianism as δ approaches 1, to dictatorship for δ = 1). For this game, we focus on the question of how a player’s position on the agenda affects his power. We also analyse the relation between the distribution of the power of individual players, the level of democracy, and the welfare efficiency of the game. Surprisingly, we find that purely democratic games are welfare inefficient due to an uneven distribution of power among the individual players. Interestingly, introducing a degree of authoritarianism into the game makes the distribution of power more equitable and maximizes welfare.