Open AccessA note on the Nash equilibria of some multi-player reachability/safety games
Author(s) -
Athanasios Kehagias
Publication year - 2022
Publication title -
journal of dynamics and games
Language(s) - English
Resource type - Journals
eISSN - 2164-6074
pISSN - 2164-6066
DOI - 10.3934/jdg.2021028
Subject(s) - reachability , nash equilibrium , mathematical economics , class (philosophy) , set (abstract data type) , best response , computer science , mathematics , strategy , simple (philosophy) , turns, rounds and time keeping systems in games , epsilon equilibrium , game theory , combinatorics , artificial intelligence , game mechanics , video game design , philosophy , epistemology , programming language
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 and ""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