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Most research done in the bargaining literature concentrates on the situations in which players get to be proposers alternately, with the first player being the proposer in the first period, the second player being the proposer in the second period, and so on until the cycle ends and the order of proposers is repeated. However, allowing for only this kind of order is a rather simplifying assumption. This paper looks at the situation in which we allow for much more general kind of protocols. We characterize the unique subgame-perfect equilibrium for two players with different discount factors, give a closed-form solution for the equilibrium payoff and finally analyze the properties of the bargaining power of the players as the function of such elements as their discount factors or their relative position and frequency of being proposers within each bargaining cycle.

Bilateral sequential bargaining with perfect information and different protocols