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Nondominated nash points: application of biobjective mixed integer programming
, Article 4OR ; 2017 , Pages 1-21 ; 16194500 (ISSN) ; Savelsbergh, M ; Talebian, M ; Sharif University of Technology
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...
Nondominated nash points: application of biobjective mixed integer programming
, Article 4OR ; Volume 16, Issue 2 , 2018 , Pages 151-171 ; 16194500 (ISSN) ; Savelsbergh, M ; Talebian, M ; Sharif University of Technology
Springer Verlag
2018
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...