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Algorithms for generalized potential games with mixed-integer variables

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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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Authors and Affiliations

  1. Department of Computer, Control and Management Engineering Antonio Ruberti, Sapienza University of Rome, Via Ariosto 25, 00185, Rome, Italy

    Simone Sagratella

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  1. Simone Sagratella
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Correspondence to Simone Sagratella.

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The work of the author has been partially supported by Avvio alla Ricerca 2015 Sapienza University of Rome, under Grant 488.

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Sagratella, S. Algorithms for generalized potential games with mixed-integer variables. Comput Optim Appl 68, 689–717 (2017). https://doi.org/10.1007/s10589-017-9927-4

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