Rejecter-proposer legislative bargaining with heterogeneous time and risk preferences

This article considers a legislative bargaining model in which the rejecter in the previous round becomes the proposer in the current round. We allow the time and risk preferences to differ across players and the voting quota to be a supermajority or submajority. We show that there exists a stationary subgame perfect equilibrium and that each player’s equilibrium payoff conditional on being a proposer is unique, and we explicitly derive the equilibria and equilibrium payoff. We compare a proposer’s equilibrium payoff when the time interval between two consecutive rounds tends to zero with respect to the protocols of the selection of proposers and the voting quota: we show that a proposer’s equilibrium payoff can be greater in this article’s rejecter-proposer model than in the Baron–Ferejohn random-proposer model; even though the voting quota increases, a proposer’s equilibrium payoff can increase.