Entropy Games

Eugene Asarin (1) , Julien Cervelle (2) , Aldric Degorre (1) , Catalin Dima (2) , Florian Horn (1) , Victor Kozyakin (3)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 LACL - Laboratoire d'Algorithmique Complexité et Logique
3 IITP - Institute for Information Transmission Problems

An entropy game is played on a finite arena by two-and-a-half players: Despot, Tribune and non-deterministic People. Whenever Despot and Tribune decide of their actions, it remains a set L of possible behaviors of People. Despot aims the entropy (growth rate) of L to be as small as possible, while Tribune wants to make it as large as possible. The main result is that the entropy game is determined, and that the optimal strategies for Despot and Tribune are positional. The analysis is based on that of matrix multiplication games, also novel and generalizing the theory of joint spectral radius.

Mots clés: game theory; entropy; joint spectral radius

Domaines: Informatique et théorie des jeux [cs.GT]; Théorie de l'information [cs.IT]

Eugene Asarin, Julien Cervelle, Aldric Degorre, Catalin Dima, Florian Horn, et al.. Entropy Games. 2015. ⟨hal-01164086v1⟩