Algorithms for generalized potential games with mixed-integer variables
We consider generalized potential games, that constitute a fundamental subclass of generalized Nash equilibrium problems. We propose different methods to compute solutions of generalized potential games with mixed-integer variables, i.e., games in which some variables are continuous while the others...
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| Vydané v: | Computational optimization and applications Ročník 68; číslo 3; s. 689 - 717 |
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| Médium: | Journal Article |
| Jazyk: | English |
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New York
Springer US
01.12.2017
Springer Nature B.V |
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| ISSN: | 0926-6003, 1573-2894 |
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| Abstract | We consider generalized potential games, that constitute a fundamental subclass of generalized Nash equilibrium problems. We propose different methods to compute solutions of generalized potential games with mixed-integer variables, i.e., games in which some variables are continuous while the others are discrete. We investigate which types of equilibria of the game can be computed by minimizing a potential function over the common feasible set. In particular, for a wide class of generalized potential games, we characterize those equilibria that can be computed by minimizing potential functions as Pareto solutions of a particular multi-objective problem, and we show how different potential functions can be used to select equilibria. We propose a new Gauss–Southwell algorithm to compute approximate equilibria of any generalized potential game with mixed-integer variables. We show that this method converges in a finite number of steps and we also give an upper bound on this number of steps. Moreover, we make a thorough analysis on the behaviour of approximate equilibria with respect to exact ones. Finally, we make many numerical experiments to show the viability of the proposed approaches. |
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| AbstractList | We consider generalized potential games, that constitute a fundamental subclass of generalized Nash equilibrium problems. We propose different methods to compute solutions of generalized potential games with mixed-integer variables, i.e., games in which some variables are continuous while the others are discrete. We investigate which types of equilibria of the game can be computed by minimizing a potential function over the common feasible set. In particular, for a wide class of generalized potential games, we characterize those equilibria that can be computed by minimizing potential functions as Pareto solutions of a particular multi-objective problem, and we show how different potential functions can be used to select equilibria. We propose a new Gauss–Southwell algorithm to compute approximate equilibria of any generalized potential game with mixed-integer variables. We show that this method converges in a finite number of steps and we also give an upper bound on this number of steps. Moreover, we make a thorough analysis on the behaviour of approximate equilibria with respect to exact ones. Finally, we make many numerical experiments to show the viability of the proposed approaches. |
| Author | Sagratella, Simone |
| Author_xml | – sequence: 1 givenname: Simone orcidid: 0000-0001-5888-1953 surname: Sagratella fullname: Sagratella, Simone email: sagratella@dis.uniroma1.it organization: Department of Computer, Control and Management Engineering Antonio Ruberti, Sapienza University of Rome |
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| SubjectTerms | Algorithms Computation Continuity (mathematics) Convex and Discrete Geometry Economic models Equilibrium Game theory Management Science Mathematics Mathematics and Statistics Multiple objective analysis Operations Research Operations Research/Decision Theory Optimization Statistics Viability |
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| Title | Algorithms for generalized potential games with mixed-integer variables |
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