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

We leave this topic Tracing back from the seminal work by Monderer and for future research. Thus, by exploiting the properties of Shapley [1], potential games represent a broad class of the ICRFs, acting as penalty terms in the individual agent's noncooperative games characterized by the existence of a BR problems, we prove that both proposed algorithms enjoy real-valued function, the potential function, such that any convergence guarantees to an equilibrium of the mixedinteger collective strategy profile minimizing the underlying function Nash equilibrium problem (MI-NEP). Specifically, coincides with a Nash equilibrium of the game. Potential in the first scenario considered the computed mixed-integer games hence provide a means to naturally model many Nash equilibrium (MI-NE) is exact, while in the second one control-theoretic applications [2] such as routing [3], complex the algorithm returns an approximate MI-NE.