A Note on the Nash Equilibria of Some Multi-Player Reachability / Safety Games
Computer Science and Game Theory
2018-10-05 v1 Discrete Mathematics
Abstract
In this short note we study a class of multi-player, turn-based games with deterministic state transitions and reachability / safety objectives (this class contains as special cases "classic" two-player reachability and safety games as well as multi-player "stay--in-a-set" and "reach-a-set" games). Quantitative and qualitative versions of the objectives are presented and for both cases we prove the existence of a deterministic and memoryless Nash equilibrium; the proof is short and simple, using only Fink's classic result about the existence of Nash equilibria for multi-player discounted stochastic games.
Keywords
Cite
@article{arxiv.1810.02194,
title = {A Note on the Nash Equilibria of Some Multi-Player Reachability / Safety Games},
author = {Athanasios Kehagias},
journal= {arXiv preprint arXiv:1810.02194},
year = {2018}
}