Power and welfare in bargaining for coalition structure formation

We investigate a noncooperative bargaining game for partitioning n agents into non-overlapping coalitions. The game has n time periods during which the players are called according to an exogenous agenda to propose offers. With probability $$\delta $$δ, the game ends during any time period $$t<n$$t<n. If it does, the first t players on the agenda get a chance to propose but the others do not. Thus, $$\delta $$δ is a measure of the degree of democracy within the game (ranging from democracy for $$\delta =0$$δ=0, through increasing levels of authoritarianism as $$\delta $$δ approaches 1, to dictatorship for $$\delta =1$$δ=1). We determine the subgame perfect equilibrium (SPE) and study how a player’s position on the agenda affects his bargaining power. We analyze the relation between the distribution of power of individual players, the level of democracy, and the welfare efficiency of the game. We find that purely democratic games are welfare inefficient and that introducing a degree of authoritarianism into the game makes the distribution of power more equitable and also maximizes welfare. These results remain invariant under two types of player preferences: one where each player’s preference is a total order on the space of possible coalition structures and the other where each player either likes or dislikes a coalition structure. Finally, we show that the SPE partition may or may not be core stable.

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