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

Filippo Fabiani; Barbara Franci; Simone Sagratella; Martin Schmidt; Mathias Staudigl

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arXiv · 2203.15410

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

Filippo Fabiani·Barbara Franci·Simone Sagratella·Martin Schmidt·Mathias Staudigl

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Abstract

We consider potential games with mixed-integer variables, for which we propose two distributed, proximal-like 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 $\epsilon$-approximate equilibrium. We corroborate our findings on a numerical instance of a Cournot oligopoly model.

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Filippo Fabiani, Barbara Franci, Simone Sagratella, Martin Schmidt, Mathias Staudigl. 2022-03-29. Proximal-like algorithms for equilibrium seeking in mixed-integer Nash equilibrium problems. https://arxiv.org/abs/2203.15410

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