We consider potential games with mixed-integer variables, for which we propose two distributed, proximallike equilibrium seeking algorithms. Specifically, we focus on two scenarios: i) the underlying game is generalized ordinal and the agents update through iterations by choosing an exact optimal strategy; ii) the game admits an exact potential and the agents adopt approximated optimal responses. By exploiting the properties of integer-compatible regularization functions used as penalty terms, we show that both algorithms converge to either an exact or an ϵ-approximate equilibrium. We corroborate our findings on a numerical instance of a Cournot oligopoly model.

Proximal-like algorithms for equilibrium seeking in mixed-integer Nash equilibrium problems

Sagratella S.;
2022-01-01

Abstract

We consider potential games with mixed-integer variables, for which we propose two distributed, proximallike equilibrium seeking algorithms. Specifically, we focus on two scenarios: i) the underlying game is generalized ordinal and the agents update through iterations by choosing an exact optimal strategy; ii) the game admits an exact potential and the agents adopt approximated optimal responses. By exploiting the properties of integer-compatible regularization functions used as penalty terms, we show that both algorithms converge to either an exact or an ϵ-approximate equilibrium. We corroborate our findings on a numerical instance of a Cournot oligopoly model.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12606/26669
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