Nash equilibrium seeking under partial-decision information: monotonicity, smoothness and proximal-point algorithms
M. Bianchi (TU Delft - Team Sergio Grammatico)
S. Grammatico (TU Delft - Team Bart De Schutter, TU Delft - Team Sergio Grammatico)
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Abstract
We consider Nash equilibrium problems in a partial-decision information scenario, where each agent can only exchange information with some neighbors, while its cost function possibly depends on the strategies of all agents. We characterize the relation between several monotonicity and smoothness assumptions postulated in the literature. Furthermore, we prove convergence of a preconditioned proximal-point algorithm, under a restricted monotonicity property that allows for a non-Lipschitz, non-continuous game mapping.