2013/10/18 by Attila Szolnoki, Matjaz Perc, Matjaž Perc · 7 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · Psychology · Social Sciences · #Evolutionary Game Theory and Cooperation #Evolutionary Psychology and Human Behavior #Experimental Behavioral Economics Studies #cs.GT #physics.soc-ph #q-bio.PE
paper · pdf · doi:10.1103/physrevx.3.041021
published as Phys. Rev. X 3 (2013) 041021 · 10 two-column pages, 10 figures; accepted for publication in Physical Review X
arxiv created 2013/10/18 · openalex publication_date 2013/11/27 · arxiv updated 2013/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Economic experiments reveal that humans value cooperation and fairness. Punishing unfair behavior is therefore common, and according to the theory of strong reciprocity, it is also directly related to rewarding cooperative behavior. However, empirical data fail to confirm that positive and negative reciprocity are correlated. Inspired by this disagreement, we determine whether the combined application of reward and punishment is evolutionary advantageous. We study a spatial public goods game, where in addition to the three elementary strategies of defection, rewarding and punishment, a fourth strategy combining the later two competes for space. We find rich dynamical behavior that gives rise to intricate phase diagrams where continuous and discontinuous phase transitions occur in succession. Indirect territorial competition, spontaneous emergence of cyclic dominance, as well as divergent fluctuations of oscillations that terminate in an absorbing phase are observed. Yet despite the high complexity of solutions, the combined strategy can survive only in very narrow and unrealistic parameter regions. Elementary strategies, either in pure or mixed phases, are much more common and likely to prevail. Our results highlight the importance of patterns and structure in human cooperation, which should be considered in future experiments.