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Statistical Physics of Human Cooperation Matjaž Perc A,B, *, Jillian J

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Statistical Physics of Human Cooperation Matjaž Perc A,B, *, Jillian J Physics Reports ( ) – Contents lists available at ScienceDirect Physics Reports journal homepage: www.elsevier.com/locate/physrep Statistical physics of human cooperation Matjaº Perc a,b, *, Jillian J. Jordan c, David G. Rand c,d,e , Zhen Wang f, Stefano Boccaletti g,h , Attila Szolnoki a,i a Faculty of Natural Sciences and Mathematics, University of Maribor, Koro²ka cesta 160, SI-2000 Maribor, Slovenia b CAMTP — Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia c Department of Psychology, Yale University, New Haven, CT 06511, USA d Department of Economics, Yale University, New Haven, CT 06511, USA e School of Management, Yale University, New Haven, CT 06511, USA f Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi'an 710072, China g CNR - Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy h The Italian Embassy in Israel, 25 Hamered st., 68125 Tel Aviv, Israel i Institute of Technical Physics and Materials Science, Centre for Energy Research, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary article info a b s t r a c t Article history: Extensive cooperation among unrelated individuals is unique to humans, who often sac- Accepted 17 May 2017 rifice personal benefits for the common good and work together to achieve what they Available online xxxx are unable to execute alone. The evolutionary success of our species is indeed due, to Editor: I. Procaccia a large degree, to our unparalleled other-regarding abilities. Yet, a comprehensive un- derstanding of human cooperation remains a formidable challenge. Recent research in the social sciences indicates that it is important to focus on the collective behavior that emerges as the result of the interactions among individuals, groups, and even societies. Non-equilibrium statistical physics, in particular Monte Carlo methods and the theory of collective behavior of interacting particles near phase transition points, has proven to be very valuable for understanding counterintuitive evolutionary outcomes. By treating models of human cooperation as classical spin models, a physicist can draw on familiar settings from statistical physics. However, unlike pairwise interactions among particles that typically govern solid-state physics systems, interactions among humans often involve group interactions, and they also involve a larger number of possible states even for the most simplified description of reality. The complexity of solutions therefore often surpasses that observed in physical systems. Here we review experimental and theoretical research that advances our understanding of human cooperation, focusing on spatial pattern formation, on the spatiotemporal dynamics of observed solutions, and on self- organization that may either promote or hinder socially favorable states. ' 2017 Elsevier B.V. All rights reserved. Contents 1. Introduction...............................................................................................................................................................................................2 1.1. Human cooperation......................................................................................................................................................................2 1.2. The role of statistical physics.......................................................................................................................................................3 2. Human experiments .................................................................................................................................................................................4 2.1. Goals of human experiments.......................................................................................................................................................4 * Corresponding author at: Faculty of Natural Sciences and Mathematics, University of Maribor, Koro²ka cesta 160, SI-2000 Maribor, Slovenia. E-mail address: [email protected] (M. Perc). http://dx.doi.org/10.1016/j.physrep.2017.05.004 0370-1573/' 2017 Elsevier B.V. All rights reserved. Please cite this article in press as: M. Perc, et al., Statistical physics of human cooperation, Physics Reports (2017), http://dx.doi.org/10.1016/j.physrep.2017.05.004. 2 M. Perc et al. / Physics Reports ( ) – 2.2. Experimental methodology.........................................................................................................................................................6 2.3. Measuring prosociality ................................................................................................................................................................6 2.3.1. Cooperation in groups ..................................................................................................................................................6 2.3.2. Cooperation in dyads....................................................................................................................................................7 2.4. Measuring the enforcement of prosociality ...............................................................................................................................7 2.4.1. Punishment in public goods games.............................................................................................................................7 2.4.2. Second-party punishment............................................................................................................................................8 2.4.3. Third-party punishment...............................................................................................................................................8 2.4.4. Rewarding .....................................................................................................................................................................9 2.5. Experiments on network effects .................................................................................................................................................9 2.6. Pitfalls and the experiment-model divide.................................................................................................................................. 10 3. Mathematical models ............................................................................................................................................................................... 10 3.1. Public goods game as the null model.......................................................................................................................................... 11 3.2. Punishment................................................................................................................................................................................... 12 3.2.1. Peer punishment........................................................................................................................................................... 12 3.2.2. Pool punishment........................................................................................................................................................... 12 3.2.3. Self-organized punishment.......................................................................................................................................... 13 3.3. Rewarding..................................................................................................................................................................................... 13 3.3.1. Peer rewarding.............................................................................................................................................................. 13 3.3.2. Pool rewarding.............................................................................................................................................................. 13 3.3.3. Self-organized rewarding............................................................................................................................................. 14 3.4. Correlated positive and negative reciprocity ............................................................................................................................. 14 3.5. Tolerance....................................................................................................................................................................................... 15 4. Monte Carlo methods ............................................................................................................................................................................... 15 4.1. Random sequential strategy updating........................................................................................................................................ 16 4.2. Random initial conditions............................................................................................................................................................ 16 4.3. Phase transitions .......................................................................................................................................................................... 18 4.4. Stability of subsystem solutions.................................................................................................................................................
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