eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-02-16
11:1
11:14
10.4230/LIPIcs.STACS.2016.11
article
Entropy Games and Matrix Multiplication Games
Asarin, Eugene
Cervelle, Julien
Degorre, Aldric
Dima, Catalin
Horn, Florian
Kozyakin, Victor
Two intimately related new classes of games are introduced and studied: entropy games (EGs) and matrix multiplication games (MMGs). An EG is played on a finite arena by two-and-a-half players: Despot, Tribune and the non-deterministic People. Despot wants to make the set of possible People's behaviors as small as possible, while Tribune wants to make it as large as possible. An MMG is played by two players that alternately write matrices from some predefined finite sets. One wants to maximize the growth rate of the product, and the other to minimize it. We show that in general MMGs are undecidable in quite a strong sense. On the positive side, EGs correspond to a subclass of MMGs, and we prove that such MMGs and EGs are determined, and that the optimal strategies are simple. The complexity of solving such games is in NP cap coNP.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol047-stacs2016/LIPIcs.STACS.2016.11/LIPIcs.STACS.2016.11.pdf
game theory
entropy
joint spectral radius