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

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 affecting the local cost function of each agent, we are able to show that both algorithms converge to either an exact or an ϵ\epsilon-approximate equilibrium. We corroborate our findings on a numerical instance of a Cournot oligopoly model.

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