Ashok Krishnan K. S., Lilou Malfoy, Helene Le Cadre, Ana Busic
原文摘要
Human agents in non cooperative games often exhibit non rational behaviour. Prospect theory provides a behavioural framework to capture how agents perceive gains and losses under risk, but, its incorporation into games typically leads to non concave and non convex utility functions, making equilibrium computation challenging. In such cases, it is difficult to obtain algorithms that have global convergence behaviour. This paper proposes a learning algorithm which uses minorization-maximization (MM). Under a proximal Polyak-Lojasiewicz (PL) condition on the potential function, we establish global convergence of the algorithm to a potential-maximizing Nash equilibrium. We further show how the structure of the MM minorizer can be used to enable a distributed implementation of the algorithm. With additional noise injection, the individual updates of the agents can be obscured, while still ensuring global convergence.
This paper considers games where the utilities for agents are the sum of a term proportional to a social utility, and another term that is an individual cost or reward. The agents are assumed to be irrational in their perception of the individual cost or reward. The multi equilibrium game is regularized, and its strictly concave potential function is used to select a unique equilibrium. This selected equilibrium is shown to be an $ε-$equilibrium of the original game, where $ε$ is parametrized by the regularizing function. A minorization-maximization based iterative learning scheme is proposed to learn equilibria in this game. This scheme converges to the potential-optimal equilibrium, and has superior convergence behavior in comparison to gradient and best response methods.