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Nondominated nash points: application of biobjective mixed integer programming

Charkhgard, H ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1007/s10288-017-0354-2
  3. Abstract:
  4. 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. © 2017 Springer-Verlag GmbH Germany
  5. Keywords:
  6. Biobjective mixed integer linear programming ; Disagreement point ; Efficient nash equilibria ; Normal form game
  7. Source: 4OR ; 2017 , Pages 1-21 ; 16194500 (ISSN)
  8. URL: https://link.springer.com/article/10.1007/s10288-017-0354-2