Commitment, Conflict, and Status Quo in Bargaining
Harry Pei
TL;DR
The paper investigates an infinite-horizon bargaining game where two players can incur a cost to commit to a share, with incompatible commitments destroying the surplus and an endogenous status quo that evolves from past divisions. It proves the existence of symmetric Markov Perfect equilibria that are asymptotically efficient and renegotiation-proof, in which players commit to fair shares in nearly all periods as patience increases and commitment costs vanish. The constructive approach uses an auxiliary mixed-strategy framework over actions $f$, $1/2$, and $1$ to sustain incentives and demonstrates that continuation values converge to the Pareto frontier, yielding near-socially optimal outcomes without Pareto-inefficient punishments. These results highlight how precedent effects and costly commitment can still support efficient dynamic bargaining in a renegotiation-proof equilibrium, with implications for legislative and contractual settings where the status quo evolves endogenously.
Abstract
Each period, two players bargain over a unit of surplus. Each player chooses between remaining flexible and committing to a take-it-or-leave-it offer at a cost. If players' committed demands are incompatible, then the current-period surplus is destroyed in the conflict. When both players are flexible, the surplus is split according to the status quo, which is the division in the last period where there was no conflict. We show that when players are patient and the cost of commitment is small, there exist a class of symmetric Markov Perfect equilibria that are asymptotically efficient and renegotiation proof, in which players commit to fair demands in almost all periods.