The representative Nash solution for two-sided bargaining problems

Imai, Haruo; Salonen, Hannu

doi:10.1016/s0165-4896(99)00035-9

Cited by 18 publications

(17 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the case where the set of feasible proposals is the unit interval, uniqueness results are given in Imai and Salonen (2000), Cho and Duggan (2003), Cardona and Ponsatí (2007), and Herings and Predtetchinski (2010). Imai and Salonen (2000) study the case where utility functions are either monotonically increasing or monotonically decreasing on the unit interval.…”

Section: Uniqueness Of the Bargaining Equilibriummentioning

confidence: 99%

“…However, the monotonicity constraints we impose imply that their assumptions on the set of feasible alternatives are violated. Other uniqueness results that have been derived in the context of one-dimensional bargaining problems, see Imai and Salonen (2000), Cho and Duggan (2003), Cardona and Ponsatí (2007), and Herings and Predtetchinski (2010) or in the context of legislative bargaining problems as in Eraslan and McLennan (2013) do not apply either. In the presence of monotonicity constraints, we can show that bargaining equilibria are unique by a contraction argument.…”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Bargaining under monotonicity constraints

Herings

Predtetchinski

2015

Econ Theory

View full text Add to dashboard Cite

We study unanimity bargaining on the division of a surplus in the presence of monotonicity constraints. The monotonicity constraints specify a complete order on the players, which has to be respected by the shares in the surplus the players obtain in any bargaining outcome. A player higher in the order should not receive a lower share of the surplus. We analyze the resulting subgame perfect equilibria in stationary strategies and show that they are characterized by the simpler notion of bargaining equilibrium. Bargaining equilibria are shown to be unique and to have the property that players ranked strictly higher obtain strictly higher shares in the surplus. The key question is whether the bargaining advantage of a higher-ranked player persists when the probability of breakdown of bargaining tends to zero. We argue that such is not the case by showing that bargaining equilibria have a unique limit equal to an equal division of the surplus. It then follows that the limit also coincides with the Nash bargaining solution for this problem.

show abstract

Section: Uniqueness Of the Bargaining Equilibriummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Bargaining under monotonicity constraints

Herings

Predtetchinski

2015

Econ Theory

View full text Add to dashboard Cite

show abstract

“…The games proposed by Chae and Yang (1994) and Suh and Wen (2006) are generalizations of Rubinstein's game along these lines. The rejecter-proposes protocol has been most widely adopted in the context of coalition formation games; examples include Chatterjee et al (1993), Bloch (1996), Ray and Vohra (1999), Imai and Salonen (2000), and Bloch and Diamantoudi (2011). Kawamori (2008) and Britz et al (2014) study more general action-dependent bargaining protocols that include the rejecter-proposes protocol as a special case.…”

Section: Introductionmentioning

confidence: 99%

A non-cooperative foundation for the continuous Raiffa solution

2017

View full text Add to dashboard Cite

This paper provides a non-cooperative foundation for (asymmetric generalizations of) the continuous Raiffa solution. Specifically, we consider a continuous-time variation of the classic Ståhl-Rubinstein bargaining model, in which there is a finite deadline that ends the negotiations, and in which each player's opportunity to make proposals is governed by a player-specific Poisson process, in that the rejecter of a proposal becomes proposer at the first next arrival of her process. Under the assumption that future payoffs are not discounted, it is shown that the expected payoffs players realize in subgame perfect equilibrium converge to the continuous Raiffa solution outcome as the deadline tends to infinity. The weights reflecting the asymmetries among the players correspond to the Poisson arrival rates of their respective proposal processes.

show abstract

“…Examples include the division of a fixed budget over two possible goals, the location of a public facility on a line, and negotiations between two firms (where a firm is viewed upon as a collection of agents with identical preferences) or between a firm and an individual about the price of a product or a service. One-dimensional bargaining problems are also studied in Banks and Duggan (2000); Imai and Salonen (2000); Cho and Duggan (2003); Cardona and Ponsatí (2007), and Herings and Predtetchinski (2010).…”

mentioning

confidence: 99%

“…We provide a linear system of characteristic equations that makes the computation of an equilibrium strategy profile an easy task. All existing uniqueness results in the one-dimensional bargaining literature (Imai and Salonen 2000;Cho and Duggan 2003;Cardona and Ponsatí 2007;Herings and Predtetchinski 2010) need the much stronger concept of subgame perfect equilibrium in stationary strategies. Surprisingly, in our model subgame perfection suffices to obtain unique predictions.…”

mentioning

confidence: 99%

Sequential share bargaining

Herings

Predtetchinski

2011

Int J Game Theory

View full text Add to dashboard Cite

This paper presents a new extension of the Rubinstein-Ståhl bargaining model to the case with n players, called sequential share bargaining. The bargaining protocol is natural and has as its main feature that the players' shares in the surplus are determined sequentially rather than simultaneously. The protocol also assumes orderly voting, a restriction on the order in which players respond to a proposal. The bargaining protocol requires unanimous agreement for proposals to be implemented. Unlike all existing bargaining protocols with unanimous agreement, the resulting game has unique subgame perfect equilibrium utilities for any value of the discount factor. The result builds on the analysis of so-called one-dimensional bargaining problems. We show that also one-dimensional bargaining problems have unique subgame perfect equilibrium utilities for any value of the discount factor.

show abstract

The representative Nash solution for two-sided bargaining problems

Cited by 18 publications

References 15 publications

Bargaining under monotonicity constraints

Bargaining under monotonicity constraints

A non-cooperative foundation for the continuous Raiffa solution

Sequential share bargaining

Contact Info

Product

Resources

About