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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Bibliographic Details
Published in:Computational optimization and applications Vol. 68; no. 3; pp. 689 - 717
Main Author: Sagratella, Simone
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2017
Springer Nature B.V
Subjects:
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
Parametric optimization
Generalized potential game
Mixed-integer nonlinear problem
Generalized Nash equilibrium problem
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary: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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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-017-9927-4