Rewarding evolutionary fitness with links between populations promotes cooperation

Evolution of cooperation in the prisoner׳s dilemma and the public goods game is studied, where initially players belong to two independent structured populations. Simultaneously with the strategy evolution, players whose current utility exceeds a threshold are rewarded by an external link to a player belonging to the other population. Yet as soon as the utility drops below the threshold, the external link is terminated. The rewarding of current evolutionary fitness thus introduces a time-varying interdependence between the two populations. We show that, regardless of the details of the evolutionary game and the interaction structure, the self-organization of fitness and reward gives rise to distinguished players that act as strong catalysts of cooperative behavior. However, there also exist critical utility thresholds beyond which distinguished players are no longer able to percolate. The interdependence between the two populations then vanishes, and cooperators are forced to rely on traditional network reciprocity alone. We thus demonstrate that a simple strategy-independent form of rewarding may significantly expand the scope of cooperation on structured populations. The formation of links outside the immediate community seems particularly applicable in human societies, where an individual is typically member in many different social networks.

[1]  F. C. Santos,et al.  Evolutionary dynamics of social dilemmas in structured heterogeneous populations. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Matjaž Perc,et al.  Sustainable institutionalized punishment requires elimination of second-order free-riders , 2012, Scientific Reports.

[3]  Michael Mesterton-Gibbons,et al.  An introduction to game-theoretic modelling , 2019 .

[4]  Arne Traulsen,et al.  Social learning promotes institutions for governing the commons , 2010, Nature.

[5]  Mason A. Porter,et al.  Multilayer networks , 2013, J. Complex Networks.

[6]  Tianguang Chu,et al.  Rare but severe concerted punishment that favors cooperation. , 2012, Theoretical population biology.

[7]  E. Hill Journal of Theoretical Biology , 1961, Nature.

[8]  Martin A. Nowak,et al.  Evolution of in-group favoritism , 2012, Scientific Reports.

[9]  Yamir Moreno,et al.  Evolutionary dynamics on interdependent populations. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Attila Szolnoki,et al.  Correlation of positive and negative reciprocity fails to confer an evolutionary advantage: Phase transitions to elementary strategies , 2013, ArXiv.

[11]  Karl Sigmund,et al.  Punish or perish? Retaliation and collaboration among humans. , 2007, Trends in ecology & evolution.

[12]  Matjaz Perc,et al.  Spreading of cooperative behaviour across interdependent groups , 2013, Scientific Reports.

[13]  Martin A. Nowak,et al.  Indirect reciprocity provides a narrow margin of efficiency for costly punishment , 2008, Nature.

[14]  Attila Szolnoki,et al.  Reward and cooperation in the spatial public goods game , 2010, ArXiv.

[15]  C. Hauert,et al.  Reward and punishment , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[16]  David G. Rand,et al.  Winners don’t punish , 2008, Nature.

[17]  David G. Rand,et al.  Anti-social Punishment Can Prevent the Co-evolution of Punishment and Cooperation , 2010 .

[18]  Hawaii,et al.  Supporting Online Material Materials and Methods Figs. S1 to S6 Tables S1 and S2 Database S1 Antisocial Punishment across Societies , 2022 .

[19]  David G. Rand,et al.  The evolution of antisocial punishment in optional public goods games. , 2011, Nature communications.

[20]  Luis Mario Floría,et al.  Evolution of Cooperation in Multiplex Networks , 2012, Scientific Reports.

[21]  M. Milinski,et al.  Volunteering leads to rock–paper–scissors dynamics in a public goods game , 2003, Nature.

[22]  David G. Rand,et al.  Human cooperation , 2013, Trends in Cognitive Sciences.

[23]  Attila Szolnoki,et al.  Optimal interdependence between networks for the evolution of cooperation , 2013, Scientific Reports.

[24]  Dirk Helbing,et al.  Globally networked risks and how to respond , 2013, Nature.

[25]  C. Hauert,et al.  Via Freedom to Coercion: The Emergence of Costly Punishment , 2007, Science.

[26]  Christian Hilbe,et al.  Incentives and opportunism: from the carrot to the stick , 2010, Proceedings of the Royal Society B: Biological Sciences.

[27]  C. D. De Dreu Human Cooperation , 2013, Psychological science in the public interest : a journal of the American Psychological Society.

[28]  F. C. Santos,et al.  Scale-free networks provide a unifying framework for the emergence of cooperation. , 2005, Physical review letters.

[29]  E. Fehr,et al.  Altruistic punishment in humans , 2002, Nature.

[30]  Attila Szolnoki,et al.  Interdependent network reciprocity in evolutionary games , 2013, Scientific Reports.

[31]  H. Ohtsuki,et al.  A simple rule for the evolution of cooperation on graphs and social networks , 2006, Nature.

[32]  M. Nowak,et al.  Evolutionary games and spatial chaos , 1992, Nature.

[33]  F. C. Santos,et al.  Social diversity promotes the emergence of cooperation in public goods games , 2008, Nature.

[34]  James H Fowler,et al.  Altruistic Punishment and the Origin of Cooperation , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[35]  Yang Li,et al.  Rejection of unfair offers in the ultimatum game is no evidence of strong reciprocity , 2012, Proceedings of the National Academy of Sciences.

[36]  G. Szabó,et al.  Evolutionary games on graphs , 2006, cond-mat/0607344.

[37]  U. Fischbacher,et al.  Strong reciprocity, human cooperation, and the enforcement of social norms , 2002, Human nature.

[38]  Attila Szolnoki,et al.  Evolutionary dynamics of group interactions on structured populations: a review , 2013, Journal of The Royal Society Interface.

[39]  Manfred Milinski,et al.  The Calculus of Selfishness , 2011 .

[40]  Attila Szolnoki,et al.  Evolution of public cooperation on interdependent networks: The impact of biased utility functions , 2012, ArXiv.

[41]  N. Christakis,et al.  Social Networks and Cooperation in Hunter-Gatherers , 2011, Nature.

[42]  D. D. de Quervain,et al.  The Neural Basis of Altruistic Punishment , 2004, Science.

[43]  L. Wang,et al.  Probabilistic interconnection between interdependent networks promotes cooperation in the public goods game , 2012, ArXiv.

[44]  Mike Mesterton-Gibbons,et al.  Cooperation Among Unrelated Individuals: Evolutionary Factors , 1992, The Quarterly Review of Biology.

[45]  B. Egloff,et al.  Need for conclusive evidence that positive and negative reciprocity are unrelated , 2013, Proceedings of the National Academy of Sciences.

[46]  Attila Szolnoki,et al.  Phase Diagrams for the Spatial Public Goods Game with Pool-Punishment , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  Torsten Röhl,et al.  An economic experiment reveals that humans prefer pool punishment to maintain the commons , 2012, Proceedings of the Royal Society B: Biological Sciences.

[48]  M. Nowak Five Rules for the Evolution of Cooperation , 2006, Science.

[49]  M. Milinski,et al.  Reputation helps solve the ‘tragedy of the commons’ , 2002, Nature.

[50]  S. Gächter,et al.  The Long-Run Benefits of Punishment , 2008, Science.

[51]  Attila Szolnoki,et al.  Information sharing promotes prosocial behaviour , 2013, ArXiv.

[52]  Bettina Rockenbach,et al.  Game theory: How to treat those of ill repute , 2008, Nature.

[53]  Zhen Wang,et al.  If players are sparse social dilemmas are too: Importance of percolation for evolution of cooperation , 2012, Scientific Reports.

[54]  David G. Rand,et al.  Positive Interactions Promote Public Cooperation , 2009, Science.

[55]  J. Gravner,et al.  Models of coalition or alliance formation. , 2011, Journal of theoretical biology.

[56]  Harry Eugene Stanley,et al.  Catastrophic cascade of failures in interdependent networks , 2009, Nature.

[57]  Attila Szolnoki,et al.  Percolation threshold determines the optimal population density for public cooperation , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[58]  Francisco C. Santos,et al.  Reward from Punishment Does Not Emerge at All Costs , 2013, PLoS Comput. Biol..

[59]  Christoph Hauert,et al.  Replicator dynamics of reward & reputation in public goods games. , 2010, Journal of theoretical biology.