On Existence, Mixtures, Computation and Efficiency in Multi-objective Games
Abstract
In a multi-objective game, each individual's payoff is a \emph{vector-valued} function of everyone's actions. Under such vectorial payoffs, Pareto-efficiency is used to formulate each individual's best-response condition, inducing Pareto-Nash equilibria as the fundamental solution concept. In this work, we follow a classical game-theoretic agenda to study equilibria. Firstly, we show in several ways that numerous pure-strategy Pareto-Nash equilibria exist. Secondly, we propose a more consistent extension to mixed-strategy equilibria. Thirdly, we introduce a measurement of the efficiency of multiple objectives games, which purpose is to keep the information on each objective: the multi-objective coordination ratio. Finally, we provide algorithms that compute Pareto-Nash equilibria and that compute or approximate the multi-objective coordination ratio.
Keywords
Cite
@article{arxiv.1809.04979,
title = {On Existence, Mixtures, Computation and Efficiency in Multi-objective Games},
author = {Anisse Ismaili},
journal= {arXiv preprint arXiv:1809.04979},
year = {2018}
}
Comments
Long version of a paper accepted to PRIMA 2018