Computing the Nash solution for scheduling bargaining problems

2009 ◽  
Vol 6 (1) ◽  
pp. 54 ◽  
Author(s):  
Alessandro Agnetis ◽  
Gianluca De Pascale ◽  
Marco Pranzo
Keyword(s):  
Nash Solution ◽  
Bargaining Problems ◽  
The Nash Solution

A Sensitivity Based Approach to Determining Non-Cooperative Solutions in Nash and Stackelberg Games

2012 ◽  
Author(s):  
Ehsan Ghotbi ◽  
Wilkistar A. Otieno ◽  
Anoop K. Dhingra
Keyword(s):  
Response Surface Methodology ◽  
Computational Effort ◽  
Stackelberg Games ◽  
Nash Solution ◽  
Numerical Errors ◽  
Multiobjective Problems ◽  
Cooperative Solutions ◽  
The One ◽  
Rational Reaction Set ◽  
The Nash Solution

A sensitivity based approach is presented to determine Nash solution(s) in multiobjective problems modeled as a non-cooperative game. The proposed approach provides an approximation to the rational reaction set (RRS) for each player. An intersection of these sets yields the Nash solution for the game. An alternate approach for generating the RRS based on design of experiments (DOE) combined with response surface methodology (RSM) is also explored. The two approaches for generating RRS are compared on three example problems to find Nash and Stackelberg solutions. It is seen that the proposed sensitivity based approach (i) requires less computational effort than a RSM-DOE approach, (ii) is less prone to numerical errors than the RSM-DOE approach, (iii) is able to find all Nash solutions when the Nash solution is not a singleton, (iv) is able to approximate non linear RRS, and (v) is able to find better a Nash solution on an example problem than the one reported in the literature.

Bargaining and Justice

1985 ◽  
Vol 2 (2) ◽  
pp. 29-47 ◽  
Author(s):  
David Gauthier
Keyword(s):  
Bargaining Problem ◽  
Nash Solution ◽  
Bargaining Process ◽  
Independence Of Irrelevant Alternatives ◽  
Principles Of Justice ◽  
The Nash Solution

My concern in this paper is with the illumination that the theory of rational bargaining sheds on the formulation of principles of justice. I shall first set out the bargaining problem, as treated in the theory of games, and the Nash solution, or solution F. I shall then argue against the axiom, labeled “independence of irrelevant alternatives,” which distinguished solution F, and also against the Zeuthen model of the bargaining process which F formalizes.

scholarly journals The Nash Solution as a von Neumann–Morgenstern Utility Function on Bargaining Games

2020 ◽  
Vol 37 (1-2) ◽  
pp. 87-104
Author(s):  
Anke Gerber
Keyword(s):  
Utility Function ◽  
Status Quo ◽  
Nash Solution ◽  
Bargaining Games ◽  
Von Neumann ◽  
Risk Neutral ◽  
The Nash Solution

AbstractIn this paper we prove that the symmetric Nash solution is a risk neutral von Neumann–Morgenstern utility function on the class of pure bargaining games. Our result corrects an error in Roth (Econometrica 46:587–594, 983, 1978) and generalizes Roth’s result to bargaining games with arbitrary status quo.

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