Nondominated Nash points: application of biobjective mixed integer programming

Hadi Charkhgard (), Martin Savelsbergh and Masoud Talebian
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Hadi Charkhgard: University of South Florida
Martin Savelsbergh: Georgia Institute of Technology
Masoud Talebian: Sharif University of Technology

4OR, 2018, vol. 16, issue 2, No 2, 171 pages

Abstract: Abstract We study the connection between biobjective mixed integer linear programming and normal form games with two players. We first investigate computing Nash equilibria of normal form games with two players using single-objective mixed integer linear programming. Then, we define the concept of efficient (Pareto optimal) Nash equilibria. This concept is precisely equivalent to the concept of efficient solutions in multi-objective optimization, where the solutions are Nash equilibria. We prove that the set of all points in the payoff (or objective) space of a normal form game with two players corresponding to the utilities of players in an efficient Nash equilibrium, the so-called nondominated Nash points, is finite. We demonstrate that biobjective mixed integer linear programming, where the utility of each player is an objective function, can be used to compute the set of nondominated Nash points. Finally, we illustrate how the nondominated Nash points can be used to determine the disagreement point of a bargaining problem.

Keywords: Biobjective mixed integer linear programming; Normal form game; Efficient Nash equilibria; Disagreement point; 90C29; 90C11; 91A05; 91-08 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10288-017-0354-2

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