eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2015-09-07
504
518
10.4230/LIPIcs.CSL.2015.504
article
Weak Subgame Perfect Equilibria and their Application to Quantitative Reachability
Brihaye, Thomas
Bruyère, Véronique
Meunier, Noémie
Raskin, Jean-Francois
We study n-player turn-based games played on a finite directed graph. For each play, the players have to pay a cost that they want to minimize. Instead of the well-known notion of Nash equilibrium (NE), we focus on the notion of subgame perfect equilibrium (SPE), a refinement of NE well-suited in the framework of games played on graphs. We also study natural variants of SPE, named weak (resp. very weak) SPE, where players who deviate cannot use the full class of strategies but only a subclass with a finite number of (resp. a unique) deviation step(s).
Our results are threefold. Firstly, we characterize in the form of a Folk theorem the set of all plays that are the outcome of a weak SPE. Secondly, for the class of quantitative reachability games, we prove the existence of a finite-memory SPE and provide an algorithm for computing it (only existence was known with no information regarding the memory). Moreover, we show that the existence of a constrained SPE, i.e. an SPE such that each player pays a cost less than a given constant, can be decided. The proofs rely on our Folk theorem for weak SPEs (which coincide with SPEs in the case of quantitative reachability games) and on the decidability of MSO logic on infinite words. Finally with similar techniques, we provide a second general class of games for which the existence of a (constrained) weak SPE is decidable.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol041-csl2015/LIPIcs.CSL.2015.504/LIPIcs.CSL.2015.504.pdf
multi-player games on graphs
quantitative objectives
Nash equilibrium
subgame perfect equilibrium
quantitative reachability