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Complexity of Spatial Games

Authors Krishnendu Chatterjee, Rasmus Ibsen-Jensen, Ismaël Jecker, Jakub Svoboda

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Author Details

Krishnendu Chatterjee
  • Institute of Science and Technology Austria, Klosterneuburg, Austria
Rasmus Ibsen-Jensen
  • University of Liverpool, UK
Ismaël Jecker
  • University of Warsaw, Poland
Jakub Svoboda
  • Institute of Science and Technology Austria, Klosterneuburg, Austria

Funding

  • Chatterjee, Krishnendu: The research was partially supported by the ERC CoG 863818 (ForM-SMArt).
  • Jecker, Ismaël: The research was partially supported by the ERC grant 950398 (INFSYS).
  • Svoboda, Jakub: The research was partially supported by the ERC CoG 863818 (ForM-SMArt).

Cite AsGet BibTex

Krishnendu Chatterjee, Rasmus Ibsen-Jensen, Ismaël Jecker, and Jakub Svoboda. Complexity of Spatial Games. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.FSTTCS.2022.11

Abstract

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.

Subject Classification

ACM Subject Classification
  • Theory of computation
Keywords
  • spatial games
  • computational complexity
  • prisoner’s dilemma
  • dynamical systems

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References

  1. Krishnendu Chatterjee, Rasmus Ibsen-Jensen, Ismaël Jecker, and Jakub Svoboda. Simplified game of life: Algorithms and complexity. In Javier Esparza and Daniel Král', editors, 45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020, August 24-28, 2020, Prague, Czech Republic, volume 170 of LIPIcs, pages 22:1-22:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.MFCS.2020.22.
  2. Xi Chen, Xiaotie Deng, and Shang-Hua Teng. Settling the complexity of computing two-player nash equilibria. Journal of the ACM (JACM), 56(3):1-57, 2009. Google Scholar
  3. Constantinos Daskalakis, Paul W. Goldberg, and Christos H. Papadimitriou. The complexity of computing a nash equilibrium. SIAM Journal on Computing, 39(1):195-259, 2009. Google Scholar
  4. Michael P. Hassell, Hugh N. Comins, and Robert M. May. Species coexistence and self-organizing spatial dynamics. Nature, 370:290-292, 1994. Google Scholar
  5. Dirk Helbing and Wenjian Yu. The outbreak of cooperation among success-driven individuals under noisy conditions. Proceedings of the National Academy of Sciences, 106(10):3680-3685, 2009. Google Scholar
  6. KM Ariful Kabir, Jun Tanimoto, and Zhen Wang. Influence of bolstering network reciprocity in the evolutionary spatial prisoner’s dilemma game: a perspective. The European Physical Journal B, 91(12), December 2018. Google Scholar
  7. Sebastián M. Ruiz. 81.27 a result on prime numbers. The Mathematical Gazette, 81:269, July 1997. URL: https://doi.org/10.2307/3619207.
  8. Martin A. Nowak and Robert M. May. Evolutionary games and spatial chaos. Nature, 359(6398):826-829, October 1992. URL: https://doi.org/10.1038/359826a0.
  9. Hisashi Ohtsuki, Christoph Hauert, Erez Lieberman, and Martin A. Nowak. A simple rule for the evolution of cooperation on graphs and social networks. Nature, 441(7092):502-505, May 2006. URL: https://doi.org/10.1038/nature04605.
  10. Hisashi Ohtsuki, Martin A. Nowak, and Jorge M. Pacheco. Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs. Phys. Rev. Lett., 98:108106, March 2007. URL: https://doi.org/10.1103/PhysRevLett.98.108106.
  11. Matjaž Perc and Attila Szolnoki. Social diversity and promotion of cooperation in the spatial prisoner’s dilemma game. Phys. Rev. E, 77:011904, January 2008. Google Scholar
  12. Matjaž Perc and Attila Szolnoki. Coevolutionary games—a mini review. Biosystems, 99(2):109-125, 2010. Google Scholar
  13. Matjaž Perc and Zhen Wang. Heterogeneous aspirations promote cooperation in the prisoner’s dilemma game. PLOS ONE, 5(12):1-8, December 2010. Google Scholar
  14. Carlos P. Roca, José A. Cuesta, and Angel Sánchez. Time scales in evolutionary dynamics. Phys. Rev. Lett., 97:158701, October 2006. Google Scholar
  15. Francisco C. Santos and Jorge M. Pacheco. Scale-free networks provide a unifying framework for the emergence of cooperation. Phys. Rev. Lett., 95, August 2005. Google Scholar
  16. Francisco C. Santos, Jorge M. Pacheco, and Tom Lenaerts. Cooperation prevails when individuals adjust their social ties. PLOS Computational Biology, 2(10):1-8, October 2006. URL: https://doi.org/10.1371/journal.pcbi.0020140.
  17. Gyorgy Szabo and Gabor Fath. Evolutionary games on graphs. Physics Reports, 446(4):97-216, 2007. Google Scholar
  18. Attila Szolnoki and Gyorgy Szabó. Cooperation enhanced by inhomogeneous activity of teaching for evolutionary prisonerquotesingles dilemma games. Europhysics Letters (EPL), 77(3):30004, January 2007. URL: https://doi.org/10.1209/0295-5075/77/30004.
  19. Mendeli H. Vainstein, Ana T.C. Silva, and Jeferson J. Arenzon. Does mobility decrease cooperation? Journal of Theoretical Biology, 244(4):722-728, 2007. Google Scholar
  20. Virgil. Eclogue IV. Cambridge University Press, 2008. Google Scholar
  21. Zhen Wang, Zhen Wang, Xiaodan Zhu, and Jeferson J. Arenzon. Cooperation and age structure in spatial games. Phys. Rev. E, 85:011149, January 2012. Google Scholar
  22. Zhi-Xi Wu, Zhihai Rong, and Petter Holme. Diversity of reproduction time scale promotes cooperation in spatial prisoner’s dilemma games. Phys. Rev. E, 80:036106, September 2009. Google Scholar
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