---
_id: '12101'
abstract:
- lang: eng
text: '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.'
acknowledgement: "Krishnendu Chatterjee: The research was partially supported by the
ERC CoG 863818\r\n(ForM-SMArt).\r\nIsmaël Jecker: The research was partially supported
by the ERC grant 950398 (INFSYS).\r\nJakub Svoboda: The research was partially supported
by the ERC CoG 863818 (ForM-SMArt)"
article_number: 11:1-11:14
article_processing_charge: No
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Rasmus
full_name: Ibsen-Jensen, Rasmus
id: 3B699956-F248-11E8-B48F-1D18A9856A87
last_name: Ibsen-Jensen
orcid: 0000-0003-4783-0389
- first_name: Ismael R
full_name: Jecker, Ismael R
id: 85D7C63E-7D5D-11E9-9C0F-98C4E5697425
last_name: Jecker
- first_name: Jakub
full_name: Svoboda, Jakub
id: 130759D2-D7DD-11E9-87D2-DE0DE6697425
last_name: Svoboda
orcid: 0000-0002-1419-3267
citation:
ama: 'Chatterjee K, Ibsen-Jensen R, Jecker IR, Svoboda J. Complexity of spatial
games. In: 42nd IARCS Annual Conference on Foundations of Software Technology
and Theoretical Computer Science. Vol 250. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik; 2022. doi:10.4230/LIPIcs.FSTTCS.2022.11'
apa: 'Chatterjee, K., Ibsen-Jensen, R., Jecker, I. R., & Svoboda, J. (2022).
Complexity of spatial games. In 42nd IARCS Annual Conference on Foundations
of Software Technology and Theoretical Computer Science (Vol. 250). Madras,
India: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.FSTTCS.2022.11'
chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, Ismael R Jecker, and Jakub
Svoboda. “Complexity of Spatial Games.” In 42nd IARCS Annual Conference on
Foundations of Software Technology and Theoretical Computer Science, Vol.
250. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. https://doi.org/10.4230/LIPIcs.FSTTCS.2022.11.
ieee: K. Chatterjee, R. Ibsen-Jensen, I. R. Jecker, and J. Svoboda, “Complexity
of spatial games,” in 42nd IARCS Annual Conference on Foundations of Software
Technology and Theoretical Computer Science, Madras, India, 2022, vol. 250.
ista: '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.'
mla: Chatterjee, Krishnendu, et al. “Complexity of Spatial Games.” 42nd IARCS
Annual Conference on Foundations of Software Technology and Theoretical Computer
Science, vol. 250, 11:1-11:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2022, doi:10.4230/LIPIcs.FSTTCS.2022.11.
short: 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.
conference:
end_date: 2022-12-20
location: Madras, India
name: 'FSTTCS: Foundations of Software Technology and Theoretical Computer Science'
start_date: 2022-12-18
corr_author: '1'
date_created: 2023-01-01T23:00:50Z
date_published: 2022-12-14T00:00:00Z
date_updated: 2026-09-16T06:59:32Z
day: '14'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.FSTTCS.2022.11
ec_funded: 1
file:
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creator: dernst
date_created: 2023-01-20T10:19:19Z
date_updated: 2023-01-20T10:19:19Z
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intvolume: ' 250'
language:
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month: '12'
oa: 1
oa_version: Published Version
project:
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
publication: 42nd IARCS Annual Conference on Foundations of Software Technology and
Theoretical Computer Science
publication_identifier:
isbn:
- '9783959772617'
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
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status: public
title: Complexity of spatial games
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...