Aspirational Bargaining ∗

This paper offers a noncooperative behaviourally-founded solution of the complete information bargaining problem where two impatient individuals wish to divide a unit pie. We formulate the game in continuous time, with unrestricted timing and content of offers. Reprising experimental work from 1960, we introduce and explore aspirational equilibrium — a Markovian refinement of subgame perfection where behaviour is governed by aspiration values (expected payoffs). The analysis is tractable, and generates many intuitive aspects of bargaining absent from the standard temporal monopoly paradigm. We find that discounted aspiration values form a martingale, and thereby compute bounds on the expected bargaining duration. We also deduce some simple implications about consecutive offers, and relate delay times, offers, and acceptance rates. Finally, we draw into question a traditional comparative static: Ceteris paribus, more impatient players can expect more of the pie. ∗We acknowledge feedback from the 2000 World Congress of Game Theory, in Bilbao, as well as theory seminars at Ohio State, Cornell, UPenn, Stanford, and Yale. Specifically, we thank Ted O’Donoghue and David Pearce for helpful comments. Ariel Rubinstein provided critical developmental feedback on a seed paper “Rethinking Bargaining” of Lones Smith, which was first presented in February 1995 at MIT. Lones acknowledges the ongoing support of the NSF. †Email: [email protected]; web: http://www.umich.edu/~lones ‡Email: [email protected]; web: http://www.econ.lsa.umich.edu/~ennio