Bargaining with durable offers and endogenous timing

Abstract

The timing structure of a bargaining game is crucial. In the static bargaining model of J. Nash (1953, Econometrica 21, 128–140), any division of the surplus is a possible equilibrium. In the alternating offer model of A. Rubinstein (1982, Econometrica 50, 97–109), there is a unique subgame perfect Nash equilibrium (SPNE). This paper takes a step toward endogenizing the timing of offers by expanding the strategy space to include the duration of the offer and permitting (but not imposing) simultaneous moves. We find that virtually any division is a possible SPNE whenever simultaneous accept/reject decisions are permitted.