Phase Diagrams for the Spatial Public Goods Game with Pool-Punishment

Physical Review E 83 (2011) 036101

11 Pages Posted: 4 Feb 2011 Last revised: 17 Jan 2012

See all articles by Attila Szolnoki

Attila Szolnoki

Hungarian Academy of Sciences (HAS) - Research Institute for Technical Physics and Materials Science

Gyorgy Szabo

Hungarian Academy of Sciences (HAS) - Research Institute for Technical Physics and Materials Science

Matjaz Perc

Faculty of Natural Sciences and Mathematics, University of Maribor

Date Written: March 7, 2011

Abstract

The efficiency of institutionalized punishment is studied by evaluating the stationary states in the spatial public goods game comprising unconditional defectors, cooperators, and cooperating pool-punishers as the three competing strategies. Fine and cost of pool-punishment are considered as the two main parameters determining the stationary distributions of strategies on the square lattice. Each player collects its payoff from five five-person public goods games, and the evolution of strategies is subsequently governed by imitation based on pairwise comparisons at a low level of noise. The impact of pool-punishment on the evolution of cooperation in structured populations is significantly different from that reported previously for peer-punishment. Representative phase diagrams reveal remarkably rich behavior, depending also on the value of the synergy factor that characterizes the efficiency of investments payed into the common pool. Besides traditional single and two-strategy stationary states, a rock-paper-scissors type cyclic dominance can emerge in strikingly different ways.

Keywords: Public Goods, Pool-Punishment, Sanctioning Institutions, Cooperation, Structured Populations, Spatial Games

JEL Classification: C7, D8, H4

Suggested Citation

Szolnoki, Attila and Szabo, Gyorgy and Perc, Matjaz, Phase Diagrams for the Spatial Public Goods Game with Pool-Punishment (March 7, 2011). Physical Review E 83 (2011) 036101, Available at SSRN: https://ssrn.com/abstract=1754589

Attila Szolnoki

Hungarian Academy of Sciences (HAS) - Research Institute for Technical Physics and Materials Science ( email )

Konkoly-Thege u. 29-33
Budapest, H-1525
Hungary

Gyorgy Szabo

Hungarian Academy of Sciences (HAS) - Research Institute for Technical Physics and Materials Science ( email )

P.O.B. 49
Budapest, H-1525
Hungary
+36-1 392-2678 (Phone)
+36-1 392-2235 (Fax)

HOME PAGE: http://www.mfa.kfki.hu/~szabo/

Matjaz Perc (Contact Author)

Faculty of Natural Sciences and Mathematics, University of Maribor ( email )

Koroska cesta 160
Maribor, SI-2000
Slovenia

HOME PAGE: http://www.matjazperc.com/

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