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Documents authored by Svoboda, Jakub


Document
Complexity of Spatial Games

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

Published in: LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)


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.

Cite as

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)


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@InProceedings{chatterjee_et_al:LIPIcs.FSTTCS.2022.11,
  author =	{Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Jecker, Isma\"{e}l and Svoboda, Jakub},
  title =	{{Complexity of Spatial Games}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.11},
  URN =		{urn:nbn:de:0030-drops-174038},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.11},
  annote =	{Keywords: spatial games, computational complexity, prisoner’s dilemma, dynamical systems}
}
Document
Simplified Game of Life: Algorithms and Complexity

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

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)


Abstract
Game of Life is a simple and elegant model to study dynamical system over networks. The model consists of a graph where every vertex has one of two types, namely, dead or alive. A configuration is a mapping of the vertices to the types. An update rule describes how the type of a vertex is updated given the types of its neighbors. In every round, all vertices are updated synchronously, which leads to a configuration update. While in general, Game of Life allows a broad range of update rules, we focus on two simple families of update rules, namely, underpopulation and overpopulation, that model several interesting dynamics studied in the literature. In both settings, a dead vertex requires at least a desired number of live neighbors to become alive. For underpopulation (resp., overpopulation), a live vertex requires at least (resp. at most) a desired number of live neighbors to remain alive. We study the basic computation problems, e.g., configuration reachability, for these two families of rules. For underpopulation rules, we show that these problems can be solved in polynomial time, whereas for overpopulation rules they are PSPACE-complete.

Cite as

Krishnendu Chatterjee, Rasmus Ibsen-Jensen, Ismaël Jecker, and Jakub Svoboda. Simplified Game of Life: Algorithms and Complexity. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 22:1-22:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{chatterjee_et_al:LIPIcs.MFCS.2020.22,
  author =	{Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Jecker, Isma\"{e}l and Svoboda, Jakub},
  title =	{{Simplified Game of Life: Algorithms and Complexity}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{22:1--22:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.22},
  URN =		{urn:nbn:de:0030-drops-126903},
  doi =		{10.4230/LIPIcs.MFCS.2020.22},
  annote =	{Keywords: game of life, cellular automata, computational complexity, dynamical systems}
}
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