Complexity of spatial games Chatterjee, Krishnendu ; https://orcid.org/0000-0002-4561-241X Ibsen-Jensen, Rasmus ; https://orcid.org/0000-0003-4783-0389 Jecker, Ismael R Svoboda, Jakub ; https://orcid.org/0000-0002-1419-3267 ddc:000 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 2022 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject conferenceObject http://purl.org/coar/resource_type/c_5794 https://research-explorer.ista.ac.at/record/12101 https://research-explorer.ista.ac.at/download/12101/12323 Chatterjee K, Ibsen-Jensen R, Jecker IR, Svoboda J. Complexity of spatial games. In: <i>42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>. Vol 250. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2022. doi:<a href="https://doi.org/10.4230/LIPIcs.FSTTCS.2022.11">10.4230/LIPIcs.FSTTCS.2022.11</a> eng info:eu-repo/semantics/altIdentifier/doi/10.4230/LIPIcs.FSTTCS.2022.11 info:eu-repo/semantics/altIdentifier/issn/1868-8969 info:eu-repo/semantics/altIdentifier/isbn/9783959772617 info:eu-repo/semantics/openAccess