Algorithms for generalized potential games with mixed-integer variables

Simone Sagratella ()
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Simone Sagratella: Sapienza University of Rome

Computational Optimization and Applications, 2017, vol. 68, issue 3, No 11, 689-717

Abstract: 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.

Keywords: Generalized Nash equilibrium problem; Generalized potential game; Mixed-integer nonlinear problem; Parametric optimization (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (16)

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DOI: 10.1007/s10589-017-9927-4

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