Bargaining with history-dependent preferences

Abstract

We study perfect information bilateral bargaining game with an infinite alternating-offers procedure, in which we add an assumption of history dependent preference. A player will devalue a share which gives her strictly lower discounted utility than what she was offered in earlier stages of the bargaining. Under the strong version of the assumption, we characterize the essentially unique subgame perfect equilibrium path, which involves considerable delay and efficiency loss. We give different interpretations of the assumption. The assumption can also be weakened under the interpretation of loss aversion. We provide a sufficient condition under which the feature of the equilibrium from strong assumption remains. JEL-codes: C72, C78.

Performance Information, Production Uncertainty, and Subjective Entitlements in Bargaining

“…In addition, salient factors of that environment (e.g., performance information and production uncertainties) can modulate bargaining outcomes and should be taken into account when modeling negotiations. Compte and Jehiel (2003) and Li (2007) model bargaining as a process where negotiators use reference points derived from past proposals when evaluating offers (see also Hyndman 2011). Their models can capture the facts that bargaining agreements are seldom immediate and that bargaining is gradual, and they formalize the idea that it may be risky to start bargaining with too generous offers.…”

“…Recent theoretical bargaining models (Compte and Jehiel 2003, Li 2007, Hyndman 2011 can account for the fact that bargaining agreement is almost never immediate but rather follows a gradual process of offers, counteroffers, and concessions. However, these models are not rich enough to be used for predictions of how entitlements will affect important elements of the bargaining process, such as opening proposals, concession behavior, and bargaining duration.…”

Envy can promote more equal division in alternating-offer bargaining.

“…Preferences in the highly stylized model only depend on the history of rejected proposals, rather than also on the bargainers' beliefs. The framework is related to Li (2007), Fershtman & Seidmann (1993) or Compte & Jehiel (2004), which assume that the bargaining history itself influences the bargainers' preferences. With reciprocal aspirations, the proposing bargainer faces a trade-off between the share he receives if the proposed partition is accepted and the worsened bargaining position due to the increase in the opponent's aspiration if the proposed share is rejected.…”

Commitment in alternating offers bargaining

“…Let us then discuss the relation to endogenous commitment models by Fershtman and Seidmann (1993) and Li (2007) (See also Compte and Jehiel, 2007). In those models, commitments are endogenous as in our model but cannot be freely chosen.…”

“…Also, unlike in Miettinen (2008, 2014), players do not commit directly to proposals in our model, but rather to veto any deal where their share is smaller than their commitment. In this respect the model resembles those of Muthoo (1992Muthoo ( , 1996 and the endogenous commitment models analyzed in Fershtman and Seidmann (1993), Li (2007), and Miettinen (2010), in which yet, the smallest acceptable shares are determined by the bargaining history in some exogenously determined way rather than freely chosen by players. Related evolutionary analyses of bargaining by Ellingsen (1997), Huck and Oechssler (1999) and Huck et al (2005) show that exogenous commitment to reject small offers improves evolutionary fitness.…”