Third-Party Intervention of Cooperation in Multilayer Networks

The conflicts in human societies have often been studied through evolutionary games. In social dilemmas, for example, individuals fair best if they defect, but the society is best off if everybody cooperates. Cooperation therefore often requires a mechanism or third parties to evolve and remain viable. To study how third parties affect the evolution of cooperation, we develop a novel game theoretic framework composed of two layers. One layer contains cooperators and defectors, while the other, the third-party layer, contains interveners. Interveners can be peacemakers, troublemakers, or a hybrid of these two. Focusing on two-player two-strategy games, we show that intervention, as an exogenous factor, can stimulate (or inhibit) cooperation by weakening (or strengthening) the dilemma strength of the game the disputant plays. Moreover, the outcome in the disputant layer that is triggered by intervention, in turn, stimulates its own evolution. We analyze the co-evolution of intervention and cooperation and find that even a minority of interveners can promote higher cooperation. By conducting stability analyses, we derive the conditions for the emergence of cooperation and intervention. Our research unveils the potential of third parties to control the evolution of cooperation.

[1]  Shaolin Tan,et al.  Consensus-Based Multipopulation Game Dynamics for Distributed Nash Equilibria Seeking and Optimization , 2023, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[2]  Jinming Du,et al.  Evolutionary dynamics of cooperation in dynamic networked systems with active striving mechanism , 2022, Applied Mathematics and Computation.

[3]  Han The Anh,et al.  Cost-efficient interventions for promoting fairness in the ultimatum game , 2021, Knowl. Based Syst..

[4]  Attila Szolnoki,et al.  Cooperator driven oscillation in a time-delayed feedback-evolving game , 2021, New Journal of Physics.

[5]  Athanasios V. Vasilakos,et al.  Distributed Population Dynamics for Searching Generalized Nash Equilibria of Population Games With Graphical Strategy Interactions , 2021, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[6]  F. C. Santos,et al.  Stable leaders pave the way for cooperation under time-dependent exploration rates , 2021, Royal Society Open Science.

[7]  Jianlei Zhang,et al.  Evolutionary Game Dynamics of Multiagent Systems on Multiple Community Networks , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[8]  Valerio Capraro,et al.  The evolution of trust and trustworthiness , 2020, Journal of the Royal Society Interface.

[9]  Jinling Liang,et al.  Evolution of cooperation under punishment. , 2020, Physical review. E.

[10]  J. Silk,et al.  Social norms and cultural diversity in the development of third-party punishment , 2020, Proceedings of the Royal Society B.

[11]  Jinming Du,et al.  Redistribution promotes cooperation in spatial public goods games under aspiration dynamics , 2019, Appl. Math. Comput..

[12]  Tong Chen,et al.  Probabilistic punishment and reward under rule of trust-based decision-making in continuous public goods game. , 2019, Journal of theoretical biology.

[13]  Attila Szolnoki,et al.  Exploring optimal institutional incentives for public cooperation , 2019, Commun. Nonlinear Sci. Numer. Simul..

[14]  Zhihai Rong,et al.  Timescale diversity facilitates the emergence of cooperation-extortion alliances in networked systems , 2019, Neurocomputing.

[15]  Bin Wu,et al.  Evolution of cooperation driven by self-recommendation. , 2019, Physical review. E.

[16]  C. D. De Dreu,et al.  The rise and fall of cooperation through reputation and group polarization , 2019, Nature Communications.

[17]  The Anh Han,et al.  Cost-effective external interference for promoting the evolution of cooperation , 2018, Scientific Reports.

[18]  Juan Wang,et al.  Role of memory effect in the evolution of cooperation based on spatial prisoner's dilemma game , 2018, Physics Letters A.

[19]  Yoh Iwasa,et al.  Exploiting a cognitive bias promotes cooperation in social dilemma experiments , 2018, Nature Communications.

[20]  Alberto Antonioni,et al.  Individual perception dynamics in drunk games , 2018, Physical review. E.

[21]  Jinming Du,et al.  Evolution of Global Cooperation in Multi-Level Threshold Public Goods Games With Income Redistribution , 2018, Front. Phys..

[22]  Attila Szolnoki,et al.  Environmental feedback drives cooperation in spatial social dilemmas , 2017, ArXiv.

[23]  Attila Szolnoki,et al.  Second-order freeriding on antisocial punishment restores the effectiveness of prosocial punishment , 2017, bioRxiv.

[24]  Zhen Wang,et al.  Evolutionary Dynamics of Collective Behavior Selection and Drift: Flocking, Collapse, and Oscillation , 2017, IEEE Transactions on Cybernetics.

[25]  E. Haruvy,et al.  The effect of third party intervention in the trust game , 2017 .

[26]  Sam P. Brown,et al.  An oscillating tragedy of the commons in replicator dynamics with game-environment feedback , 2016, Proceedings of the National Academy of Sciences.

[27]  S. Kokubo,et al.  Universal scaling for the dilemma strength in evolutionary games. , 2015, Physics of life reviews.

[28]  N. Halevy,et al.  Selfish third parties act as peacemakers by transforming conflicts and promoting cooperation , 2015, Proceedings of the National Academy of Sciences.

[29]  Lin Wang,et al.  Evolutionary games on multilayer networks: a colloquium , 2015, The European Physical Journal B.

[30]  Xiang Li,et al.  When Reputation Enforces Evolutionary Cooperation in Unreliable MANETs , 2014, IEEE Transactions on Cybernetics.

[31]  Lin Wang,et al.  Degree mixing in multilayer networks impedes the evolution of cooperation , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Philipp Lergetporer,et al.  Third-party punishment increases cooperation in children through (misaligned) expectations and conditional cooperation , 2014, Proceedings of the National Academy of Sciences.

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

[34]  Xiang Li,et al.  Towards a Snowdrift Game Optimization to Vertex Cover of Networks , 2013, IEEE Transactions on Cybernetics.

[35]  N. Nikiforakis,et al.  Mixing the carrots with the sticks: third party punishment and reward , 2013, Experimental Economics.

[36]  F. C. Santos,et al.  Evolutionary dynamics of collective action in N-person stag hunt dilemmas , 2009, Proceedings of the Royal Society B: Biological Sciences.

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

[38]  S. Assenza,et al.  Enhancement of cooperation in highly clustered scale-free networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[40]  C. Hauert,et al.  Models of cooperation based on the Prisoner's Dilemma and the Snowdrift game , 2005 .

[41]  C. Hauert,et al.  Game theory and physics , 2005 .

[42]  C. Hauert,et al.  Replicator dynamics for optional public good games. , 2002, Journal of theoretical biology.

[43]  R. Burt,et al.  Kinds of Third-Party Effects on Trust , 1995 .

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

[45]  Roger Ware,et al.  Evolutionary stability in the repeated prisoner's dilemma , 1989 .

[46]  U. Dieckmann,et al.  Electronic supplementary material for Parent-preferred dispersal promotes cooperation in structured populations , 2018 .

[47]  Ashkan Hafezalkotob,et al.  Direct and indirect intervention schemas of government in the competition between green and non-green supply chains , 2018 .

[48]  Nir Halevy,et al.  Third parties promote cooperative norms in repeated interactions , 2017 .

[49]  A. Griffin,et al.  Social semantics : altruism , cooperation , mutualism , strong reciprocity and group selection , 2007 .

[50]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[51]  A. Rapoport.  Game theory as a theory of conflict resolution , 1974 .