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We consider potential games with mixed-integer variables, for which wepropose two distributed, proximal-like equilibrium seeking algorithms.Specifically, we focus on two scenarios: i) the underlying game is generalizedordinal and the agents update through iterations by choosing an exact optimalstrategy; ii) the game admits an exact potential and the agents adoptapproximated optimal responses. By exploiting the properties ofinteger-compatible regularization functions used as penalty terms, we show thatboth algorithms converge to either an exact or an $\epsilon$-approximateequilibrium. We corroborate our findings on a numerical instance of a Cournotoligopoly model.

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