License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2022.11
URN: urn:nbn:de:0030-drops-174038
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17403/
Chatterjee, Krishnendu ;
Ibsen-Jensen, Rasmus ;
Jecker, Ismaël ;
Svoboda, Jakub
Complexity of Spatial Games
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.
BibTeX - Entry
@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/opus/volltexte/2022/17403},
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}
}
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Keywords: |
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spatial games, computational complexity, prisoner’s dilemma, dynamical systems |
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Collection: |
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42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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14.12.2022 |
