Recognition without replacement in legislative bargaining

This paper studies infinite-horizon sequential bargaining among n >= 3 players in which a proposer is randomly selected from the pool of potential proposers. If the proposal is rejected, the current and previous proposers are excluded from the pool of potential proposers, and the game moves on to the next round until every player has had the same number of opportunities to be the proposer. To analyze the model with a particular time dependency within each sequence of n rounds (a cycle), I characterize the stationary equilibrium of a stochastic game, which I call cycle-stationary subgame perfect (CSSP) equilibrium. The CSSP equilibrium is unique in payoffs and analogous to the subgame perfect equilibrium of some forms of finite-horizon bargaining. Even when every player is entirely patient, the proposer's share in the CSSP equilibrium is smaller than that predicted by the stationary equilibrium of the Baron-Ferejohn legislative bargaining model. (C) 2019 Elsevier Inc. All rights reserved.