A New (Simplified) Derivation of Nash’s Bargaining Solution

Hoang Phuong Nguyen; Laxman Bokati; Vladik Kreinovich

doi:10.20965/jaciii.2020.p0589

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JACIII Vol.24 No.5 pp. 589-592

doi: 10.20965/jaciii.2020.p0589

(2020)

Paper:

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A New (Simplified) Derivation of Nash’s Bargaining Solution

Hoang Phuong Nguyen^*,†, Laxman Bokati^, and Vladik Kreinovich^,***

^*Division Informatics, Math-Informatics Faculty, Thang Long University
Nghiem Xuan Yem Road, Hoang Mai District, Hanoi, Vietnam

^**Computational Science Program, University of Texas at El Paso
500 West University Avenue, El Paso, Texas 79968, USA

^***Department of Computer Science, University of Texas at El Paso
500 West University Avenue, El Paso, Texas 79968, USA

^†Corresponding author

Received:

March 4, 2020

Accepted:

April 15, 2020

Published:

September 20, 2020

Keywords:

group decision making, Nash’s bargaining solution, partial order

Abstract

According to the Nobelist John Nash, if a group of people wants to selects one of the alternatives in which all of them get a better deal than in a status quo situations, then they should select the alternative that maximizes the product of their utilities. In this paper, we provide a new (simplified) derivation of this result, a derivation which is not only simpler – it also does not require that the preference relation between different alternatives be linear.

Cite this article as:

H. Nguyen, L. Bokati, and V. Kreinovich, “A New (Simplified) Derivation of Nash’s Bargaining Solution,” J. Adv. Comput. Intell. Intell. Inform., Vol.24 No.5, pp. 589-592, 2020.

Data files:

References

[1] J. F. Nash, Jr., “The Bargaining Problem,” Econometrica, Vol.18, Issue 2, pp. 155-162, 1950.
[2] P. C. Fishburn, “Utility Theory for Decision Making,” John Wiley & Sons Inc., 1969.
[3] V. Kreinovich, “Decision Making Under Interval Uncertainty (and Beyond),” P. Guo and W. Pedrycz (Eds.), “Human-Centric Decision-Making Models for Social Sciences,” pp. 163-193, Springer, 2014.
[4] R. D. Luce and R. Raiffa, “Games and Decisions: Introduction and Critical Survey,” Dover, 1989.
[5] H. T. Nguyen, O. Kosheleva, and V. Kreinovich, “Decision making beyond Arrow’s “impossibility theorem,” with the analysis of effects of collusion and mutual attraction,” Int. J. of Intelligent Systems, Vol.24, Issue 1, pp. 27-47, 2009.
[6] H. Raiffa, “Decision Analysis: Introductory Lectures on Choices under Uncertainty,” McGraw-Hill College, 1997.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] J. F. Nash, Jr., “The Bargaining Problem,” Econometrica, Vol.18, Issue 2, pp. 155-162, 1950.

[2] [2] P. C. Fishburn, “Utility Theory for Decision Making,” John Wiley & Sons Inc., 1969.

[3] [3] V. Kreinovich, “Decision Making Under Interval Uncertainty (and Beyond),” P. Guo and W. Pedrycz (Eds.), “Human-Centric Decision-Making Models for Social Sciences,” pp. 163-193, Springer, 2014.

[4] [4] R. D. Luce and R. Raiffa, “Games and Decisions: Introduction and Critical Survey,” Dover, 1989.

[5] [5] H. T. Nguyen, O. Kosheleva, and V. Kreinovich, “Decision making beyond Arrow’s “impossibility theorem,” with the analysis of effects of collusion and mutual attraction,” Int. J. of Intelligent Systems, Vol.24, Issue 1, pp. 27-47, 2009.

[6] [6] H. Raiffa, “Decision Analysis: Introductory Lectures on Choices under Uncertainty,” McGraw-Hill College, 1997.

A New (Simplified) Derivation of Nash’s Bargaining Solution

Hoang Phuong Nguyen*,†, Laxman Bokati**, and Vladik Kreinovich**,***

Hoang Phuong Nguyen^*,†, Laxman Bokati^, and Vladik Kreinovich^,***