conference paper published yes Krishnendu Chatterjee author 2E5DCA20-F248-11E8-B48F-1D18A9856A870000-0002-4561-241X Rasmus Ibsen-Jensen author 3B699956-F248-11E8-B48F-1D18A9856A870000-0003-4783-0389 Ismael R Jecker author 85D7C63E-7D5D-11E9-9C0F-98C4E5697425 Jakub Svoboda author 130759D2-D7DD-11E9-87D2-DE0DE66974250000-0002-1419-3267 KrCh department FSTTCS: Foundations of Software Technology and Theoretical Computer Science Formal Methods for Stochastic Models: Algorithms and Applications project 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. https://research-explorer.ista.ac.at/download/12101/12323/2022_LIPICs_Chatterjee.pdf application/pdfno Schloss Dagstuhl - Leibniz-Zentrum für Informatik2022Madras, India eng 1868-8969 978395977261710.4230/LIPIcs.FSTTCS.2022.11 250 https://research-explorer.ista.ac.at/record/20138 K. Chatterjee, R. Ibsen-Jensen, I.R. Jecker, J. Svoboda, in:, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. Chatterjee, K., Ibsen-Jensen, R., Jecker, I. R., &#38; Svoboda, J. (2022). Complexity of spatial games. In <i>42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i> (Vol. 250). Madras, India: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href="https://doi.org/10.4230/LIPIcs.FSTTCS.2022.11">https://doi.org/10.4230/LIPIcs.FSTTCS.2022.11</a> Chatterjee K, Ibsen-Jensen R, Jecker IR, Svoboda J. 2022. Complexity of spatial games. 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. FSTTCS: Foundations of Software Technology and Theoretical Computer Science vol. 250, 11:1-11:14. 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> Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, Ismael R Jecker, and Jakub Svoboda. “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. <a href="https://doi.org/10.4230/LIPIcs.FSTTCS.2022.11">https://doi.org/10.4230/LIPIcs.FSTTCS.2022.11</a>. Chatterjee, Krishnendu, et al. “Complexity of Spatial Games.” <i>42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>, vol. 250, 11:1-11:14, 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>. K. Chatterjee, R. Ibsen-Jensen, I. R. Jecker, and J. Svoboda, “Complexity of spatial games,” in <i>42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>, Madras, India, 2022, vol. 250. 121012023-01-01T23:00:50Z2026-07-27T12:52:03Z