2026-07-22T15:33:24Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17403 2024-03-06T10:59:40Z ddc:004 open_access

Complexity of Spatial Games Chatterjee, Krishnendu Ibsen-Jensen, Rasmus Jecker, Ismaël Svoboda, Jakub spatial games computational complexity prisoner’s dilemma dynamical systems Spatial games form a widely-studied class of games from biology and physics modeling the evolution of social behavior. Formally, such a game is defined by a square (d by d) payoff matrix M and an undirected graph G. Each vertex of G represents an individual, that initially follows some strategy i ∈ {1,2,…,d}. In each round of the game, every individual plays the matrix game with each of its neighbors: An individual following strategy i meeting a neighbor following strategy j receives a payoff equal to the entry (i,j) of M. Then, each individual updates its strategy to its neighbors' strategy with the highest sum of payoffs, and the next round starts. The basic computational problems consist of reachability between configurations and the average frequency of a strategy. For general spatial games and graphs, these problems are in PSPACE. In this paper, we examine restricted setting: the game is a prisoner’s dilemma; and G is a subgraph of grid. We prove that basic computational problems for spatial games with prisoner’s dilemma on a subgraph of a grid are PSPACE-hard. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Krishnendu Chatterjee and Rasmus Ibsen-Jensen and Ismaël Jecker and Jakub Svoboda 2022 Is Part Of LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2022.11 urn:nbn:de:0030-drops-174038 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.11 eng https://creativecommons.org/licenses/by/4.0/legalcode