Robustness of intermediate agreements and bargaining solutions

Anbarcı, Nejat; Sun, Ching-jen

doi:10.1016/j.geb.2012.11.001

Cited by 19 publications

(8 citation statements)

References 14 publications

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“…(2) x > d for some x ∈ S It will be convenient to consider also˜ , the set of all bargaining problems satisfying just (1).…”

Section: Letmentioning

confidence: 99%

Robustness of intermediate agreements for the discrete Raiffa solution

Trockel

2014

Games and Economic Behavior

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These notes consist of two parts. In the first one I present a counter example to Proposition 3 of Anbarci & Sun (2013). In the second part I propose a correction based on an axiom similar to one used by Salonen (1988) in the first axiomatization of the Discrete Raiffa solution. * Counterexample and correction for Proposition 3 in N. Anbarci and C.-j. Sun (2013): Robustness of Intermediate Agreements and Bargaining Solutions Games and Economic Behavior, 77,[367][368][369][370][371][372][373][374][375][376] Basic Definitions and AxiomsThis section is mainly an extract of relevant parts of the respective section in Anbarci and Sun (2013) supplemented by some remarks and an axiom from Salonen (1988). Basic DefinitionsAn n-person (bargaining) problem is a pair (S, d), where S ⊂ R n is the set of utility possibilities that the players can achieve through cooperation and d ∈ S is the disagreement point, which is the utility allocation that results if no agreement is reached. For all S, let IR(S, d) := {x ∈ S|x ≥ d} be the set of individually rational utility allocations. Letbe the class of all n-person problems satisfying the following:(1) The set S is compact, convex and comprehensive.(2) x > d for some x ∈ S It will be convenient to consider also˜ , the set of all bargaining problems satisfying just(1).Denote the ideal point of (S,Denote by b and m the restrictions ofb andm to ⊂˜ , respectively.A solution on˜ is a functionf :˜ −→ R n such that for all (S, d) ∈˜ we havẽ f (S, d) ∈ S. The restriction off to ⊂˜ is denoted f and is called a solution on .Consider any bargaining problem (S, d) ∈˜ . The game (H S , d) ∈˜ defined by H S : = co {d,b 1 (S, d)e 1 , ...,b n (S, d)e n }, with e i , i = 1, ..., n the canonical unit vectors of R n , is the "largest hyperplane game contained" in (S, d). The game (H S ,m(S, d)) is an element of˜ \ . Given any bargaining problem (S, d) ∈and a solution f :Notice, that this definition employed by Anbarci and Sun (2013) makes use of the assumption that (S, d ) ∈ . Therefore for the game AxiomsFirst I introduce the three axioms of Anbarci and Sun (2013) relevant for my analysis.Then I formulate for the present context and in the present terminology of Anbarci and Sun an axiom due to Salonen (1988) that is crucial for the announced correction in the second part of this note. Let f : −→ R n be a solution on . Midpoint Domination (MD)Independence of Non-Midpoint-Dominating Alternatives (INMD):As Anbarci and Sun (2013) stress the hypothesis of INMD implies: Salonen (1988) was the first article to my best knowledge that provided in his Theorem 2 an axiomatization of the Discrete Raiffa solution on the set˜ of bargaining problems. The three axioms he is using are anonymity, covariance under affine transformations and an axiom, that he called Second Decomposability axiom. Robustness of Intermediate Agreements in theIn the context of rather than˜ and the terminology of Anbarci and Sun this axiom can be restated as:Based on this insight an axiomatization of the Raiffa solution via repeat...

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“…(2) x > d for some x ∈ S It will be convenient to consider also˜ , the set of all bargaining problems satisfying just (1).…”

Section: Letmentioning

confidence: 99%

Robustness of intermediate agreements for the discrete Raiffa solution

Trockel

2014

Games and Economic Behavior

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“…The axiom of step-by-step negotiation in Kalai's paper states that certain types of decompositions of the bargaining set result in the same solution to the problem. Later work emphasizes axioms that involve the change of a disagreement point while keeping the bargaining set fixed (Thomson, 1987;Peters and van Damme, 1991;Livne, 1989;Anbarci and Sun, 2009;Trockel, 2009). In particular, properties of the set of disagreement points that do not change the solution were studied in some of these works.…”

Section: Related Workmentioning

confidence: 99%

“…Livne (1989) and Peters and van Damme (1991) axiomatize the continuous Raiffa solution for two-person bargaining problems. More recently, Anbarci and Sun (2009) propose an axiomatization of the discrete Raiffa solution for the two-person case. These works axiomatize the solution, but not the process itself.…”

Section: Related Workmentioning

confidence: 99%

Generalized Raiffa solutions

Diskin¹,

Koppel²,

Samet³

2011

Games and Economic Behavior

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We define a family of solutions for n-person bargaining problems which generalizes the discrete Raiffa solution and approaches the continuous Raiffa solution. Each member of this family is a stepwise solution, which is a pair of functions: a step-function that determines a new disagreement point for a given bargaining problem, and a solution function that assigns the solution to the problem. We axiomatically characterize stepwise solutions of the family of generalized Raiffa solutions, using standard axioms of bargaining theory.

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“…They defined a family of discrete solutions for N-person bargaining problems which approaches the continuous Raiffa solution as the step size gradually becomes smaller. [17] proposed a unified framework for characterizations of different axioms that lead to different bargaining solutions. Their solution was simplified by [18] who also filled in a gap in the proof.…”

Section: Introductionmentioning

confidence: 99%

On the Allocation of Multiple Divisible Assets to Players with Different Utilities

Zehavi

Leshem

2017

Comput Econ

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When there is a dispute between players on how to divide multiple divisible assets, how should it be resolved? In this paper we introduce a multi-asset game model that enables cooperation between multiple agents who bargain on sharing K assets, when each player has a different value for each asset. It thus extends the sequential discrete Raiffa solution and the Talmud rule solution to multi-asset cases.

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Robustness of intermediate agreements and bargaining solutions

Cited by 19 publications

References 14 publications

Robustness of intermediate agreements for the discrete Raiffa solution

Robustness of intermediate agreements for the discrete Raiffa solution

Generalized Raiffa solutions

On the Allocation of Multiple Divisible Assets to Players with Different Utilities

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