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Subgame Perfect Equilibrium in a Bargaining Model with Deterministic Procedures

Mao, Liang (2015): Subgame Perfect Equilibrium in a Bargaining Model with Deterministic Procedures.

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Abstract

Two players, $A$ and $B$, bargain to divide a perfectly divisible pie. In a bargaining model with constant discount factors, $\delta_A$ and $\delta_B$, we extend \cite{Rubinstein82}'s alternating offers procedures to more general deterministic procedures so that any player in any period can be the proposer. We show that each bargaining game with a deterministic procedure has a unique subgame perfect equilibrium (SPE) payoff outcome, which is efficient. Conversely, each efficient division of the pie can be supported as an SPE outcome by some procedure if $\delta_A+\delta_B\geq 1$, while almost no division can ever be supported in SPE if $\delta_A+\delta_B < 1$.

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