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Cited by 417

The DOI matches its Crossref record; 44 of the 44 references it cites were found in a registry or an index.

Punish, but not too hard: how costly punishment spreads in the spatial public goods game

Open access
Helbing, Dirk, Szolnoki, Attila, Perc, Matjaž, Szabó, György·2010·New Journal of Physics
DOI 10.1088/1367-2630/12/8/083005
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Abstract

We study the evolution of cooperation in spatial public goods games where, besides the classical strategies of cooperation (C) and defection (D), we consider punishing cooperators (PC) or punishing defectors (PD) as an additional strategy. Using a minimalist modeling approach, our goal is to separately clarify and identify the consequences of the two punishing strategies. Since punishment is costly, punishing strategies lose the evolutionary competition in case of well-mixed interactions. When spatial interactions are taken into account, however, the outcome can be strikingly different, and cooperation may spread. The underlying mechanism depends on the character of the punishment strategy. In the case of cooperating punishers, increasing the fine results in a rising cooperation level. In contrast, in the presence of the PD strategy, the phase diagram exhibits a reentrant transition as the fine is increased. Accordingly, the level of cooperation shows a non-monotonous dependence on the fine. Remarkably, punishing strategies can spread in both cases, but based on largely different mechanisms, which depend on the cooperativeness (or not) of punishers.

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Metadata

Authors
Helbing, D., Szolnoki, A., Perc, M., & Szabó, G.
Venue
New Journal of Physics
Publisher
IOP Publishing
Published
2010-08-03
Volume
12
Issue
8
Pages
083005
ISSN
1367-2630 (ISSN-L)
DOI
10.1088/1367-2630/12/8/083005
OpenAlex
W2113962824
Cited by
417
References
44
FWCI
61.56
Type
journal article
Language
en
Open access
gold

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CoChat. (2026). Citation check: Punish, but not too hard: how costly punishment spreads in the spatial public goods game. https://app.cochat.ai/papers/10.1088/1367-2630/12/8/083005
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Helbing, D., Szolnoki, A., Perc, M., & Szabó, G. (2010). Punish, but not too hard: how costly punishment spreads in the spatial public goods game. New Journal of Physics. https://doi.org/10.1088/1367-2630/12/8/083005

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