Envy can promote more equal division in alternating-offer bargaining

Abstract

Bargainers in an open-ended, alternating-offer bargaining situation may perceive envy, a utility loss caused by receiving the smaller share, which is modeled in some social preferences in addition to self-interest. I extend Rubinstein's (1982) original solution of the bargaining problem for two self-interested bargainers to this strategic situation. Bargainers still reach agreement in the first period and their bargaining shares increase with the strength of their own envy. As both bargainers' envy diminishes, the agreed partition converges to the Rubinstein division. If equally patient bargaining parties exhibit similar envy, then the agreed partition is tilted away from the Rubinstein division toward the equal division. Notably, the potential sensation of envy also boosts the share of the eventually envy-free party who leaves the bargaining with the larger share under the agreed partition. This gain in bargaining strength through envy can result in a bargaining outcome that is more unequal than predicted by the Rubinstein division.