Intrinsic Comparative Statics of a Nash Bargaining Solution

2016 ◽  
Vol 18 (04) ◽  
pp. 1650013
Author(s):  
Michael R. Caputo
Keyword(s):  
Basic Result ◽  
Nondecreasing Function ◽  
Positive Semidefinite ◽  
Nash Bargaining Solution ◽  
Comparative Statics ◽  
Nash Bargaining ◽  
Bargaining Solution ◽  
Sensitivity Matrix ◽  
Disagreement Point ◽  
Bargaining Problems

A generalization of the class of bargaining problems examined by Engwerda and Douven [(2008) On the sensitivity matrix of the Nash bargaining solution, Int. J. Game Theory 37, 265–279] is studied. The generalized class consists of nonconvex bargaining problems in which the feasible set satisfies the requirement that the set of weak Pareto-optimal solutions can be described by a smooth function. The intrinsic comparative statics of the aforesaid class are derived and shown to be characterized by a symmetric and positive semidefinite matrix, and an upper bound to the rank of the matrix is established. A corollary to this basic result is that a Nash bargaining solution is intrinsically a locally nondecreasing function of its own disagreement point. Other heretofore unknown results are similarly deduced from the basic result.

scholarly journals Negotiating transfer pricing using the Nash bargaining solution

2017 ◽  
Vol 27 (4) ◽  
pp. 853-864 ◽  
Author(s):  
Julio B. Clempner ◽  
Alexander S. Poznyak
Keyword(s):  
Transfer Pricing ◽  
Optimization Method ◽  
Nash Bargaining Solution ◽  
Transfer Price ◽  
Point Of View ◽  
Nash Bargaining ◽  
Bargaining Solution ◽  
Theory Approach ◽  
Disagreement Point ◽  
Nash Bargaining Game

AbstractThis paper analyzes and proposes a solution to the transfer pricing problem from the point of view of the Nash bargaining game theory approach. We consider a firm consisting of several divisions with sequential transfers, in which central management provides a transfer price decision that enables maximization of operating profits. Price transferring between divisions is negotiable throughout the bargaining approach. Initially, we consider a disagreement point (status quo) between the divisions of the firm, which plays the role of a deterrent. We propose a framework and a method based on the Nash equilibrium approach for computing the disagreement point. Then, we introduce a bargaining solution, which is a single-valued function that selects an outcome from the feasible pay-offs for each bargaining problem that is a result of cooperation of the divisions of the firm involved in the transfer pricing problem. The agreement reached by the divisions in the game is the most preferred alternative within the set of feasible outcomes, which produces a profit-maximizing allocation of the transfer price between divisions. For computing the bargaining solution, we propose an optimization method. An example illustrating the usefulness of the method is presented.

scholarly journals Risk aversion for losses and the Nash bargaining solution

2021 ◽  
Author(s):  
Hans Peters
Keyword(s):  
Risk Aversion ◽  
Decision Maker ◽  
Nash Bargaining Solution ◽  
Axiomatic Characterization ◽  
Nash Bargaining ◽  
Bargaining Solution ◽  
Risk Averse ◽  
Disagreement Point ◽  
Theoretic Characterization

AbstractWe call a decision maker risk averse for losses if that decision maker is risk averse with respect to lotteries having alternatives below a given reference alternative in their support. A two-person bargaining solution is called invariant under risk aversion for losses if the assigned outcome does not change after correcting for risk aversion for losses with this outcome as pair of reference levels, provided that the disagreement point only changes proportionally. We present an axiomatic characterization of the Nash bargaining solution based on this condition, and we also provide a decision-theoretic characterization of the concept of risk aversion for losses.

Legal Hold-up in Cotenancy

2003 ◽  
Vol 3 (1) ◽  
Author(s):  
Manel Baucells ◽  
Steven A. Lippman
Keyword(s):  
Nash Bargaining Solution ◽  
Nash Bargaining ◽  
Bargaining Solution ◽  
Disagreement Point ◽  
Fixed Price ◽  
Poisson Arrival ◽  
Credible Threat ◽  
Legal Costs ◽  
Reasonable Answers ◽  
The Impact

Abstract Our analysis (Baucells and Lippman [2001]) of the problem of legal hold-up in co-ownership, in which legal partition is the only remedy to force a sale, proceeded as if a sale of the asset could be effected at any time at a fixed price if the cotenants agree. Here we utilize the more realistic assumption that potential buyers appear intermittently (in accord with a Poisson process and that the price offered is drawn from a specified distribution). In applying the Nash bargaining solution, we select the disagreement point in accord either with Nash's methodology of rational threats or with reservation values. While neither methodology for selecting the disagreement point produces a credible threat when the agents incur legal costs, we argue that the rational threats approach produces more reasonable answers. Our main analysis considers the impact of a Poisson arrival of offers and an exponential time to court upon the optimal bargaining strategies of the cotenants.

The (Stabilized) Nash Bargaining Solution as a Principle of Distributive Justice

Utilitas ◽  
2010 ◽  
Vol 22 (4) ◽  
pp. 447-473 ◽  
Author(s):  
MICHAEL MOEHLER
Keyword(s):  
Distributive Justice ◽  
Moral Reasoning ◽  
Bargaining Power ◽  
Nash Bargaining Solution ◽  
Nash Bargaining ◽  
Original Position ◽  
Bargaining Solution ◽  
Moral Intuitions ◽  
Instrumental Reasoning ◽  
Relative Bargaining Power

It is argued that the Nash bargaining solution cannot serve as a principle of distributive justice because (i) it cannot secure stable cooperation in repeated interactions and (ii) it cannot capture our moral intuitions concerning distributive questions. In this article, I propose a solution to the first problem by amending the Nash bargaining solution so that it can maintain stable cooperation among rational bargainers. I call the resulting principle the stabilized Nash bargaining solution. The principle defends justice in the form ‘each according to her basic needs and above this level according to her relative bargaining power’. In response to the second problem, I argue that the stabilized Nash bargaining solution can serve as a principle of distributive justice in certain situations where moral reasoning is reduced to instrumental reasoning. In particular, I argue that rational individuals would choose the stabilized Nash bargaining solution in Rawls’ original position.

Dynamic Subcarrier and Power Allocation Based on Nash Bargaining Solution in Symmetric Cooperative OFDMA Networks

2011 ◽  
Vol 187 ◽  
pp. 510-515
Author(s):  
Wei Liu ◽  
Jing Min Tang
Keyword(s):  
Power Allocation ◽  
Nash Bargaining Solution ◽  
Nash Bargaining ◽  
Bargaining Solution ◽  
Subcarrier Allocation ◽  
Allocation Scheme ◽  
Allocation Algorithm ◽  
Cooperative Scheme ◽  
Joint Resource Allocation ◽  
Adaptive Power

In this paper, subcarrier and power allocation are jointly considered in a three-node symmetric cooperation orthogonal frequency-division multiple access uplink system. With the help of Nash bargaining solution, the dynamic subcarrier allocation scheme and the adaptive power allocation scheme are proposed for joint optimization. The joint resource allocation is decomposed and solved by dynamic subcarrier allocation algorithm and adaptive power allocation algorithm. Simulation results show the effectiveness of the proposed cooperative scheme.

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