2022/03/29 by Fabiani, Filippo, Franci, Barbara, Sagratella, Simone +2 · 1 citation
#Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Multiagent Systems (cs.MA) #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2203.15410
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 ε-approximate equilibrium. We corroborate our findings on a numerical instance of a Cournot oligopoly model.