Coalition-then-allocation legislative bargaining

Abstract

We investigate legislative bargaining where players first bargain over coalitions and after one coalition is formed, players in this coalition bargain over allocations. We show that if discount factors in coalition bargaining are smaller than those in allocation bargaining and sufficiently large, in any stationary subgame perfect equilibrium (SSPE), relatively impatient proposers immediately form a minimal winning coalition of relatively impatient players, but relatively patient proposers fail to form a coalition and bargaining delays occur. We also show that if the discount factors in coalition bargaining are smaller than those in allocation bargaining and sufficiently small, delays do not occur. Furthermore, we show that if the discount factors in allocation bargaining are smaller than those in coalition bargaining and sufficiently similar across players, there exist multiple SSPEs exhibiting delays and having different payoff tuples. We also introduce leader-dependent hedonic games, where each player has a preference relation over pairs of a coalition and its leader. We view a truncated game with replacing subgames of allocation bargaining by their SSPE playoff tuples to be based on a leader-dependent hedonic game.