Adaptive willingness resolves social dilemma in network populations.

Cooperation is an effective manner to enable different elements of complex networks to work well. In this work, we propose a coevolution mechanism of learning willingness in the network population: an agent will be more likely to imitate a given neighbor's strategy if her payoff is not less than the average performance of all her neighbors. Interestingly, increase of learning willingness will greatly promote cooperation even under the environment of extremely beneficial temptation to defectors. Through a microscopic analysis, it is unveiled that cooperators are protected due to the appearance of large-size clusters. Pair approximation theory also validates all these findings. Such an adaptive mechanism thus provides a feasible solution to relieve social dilemmas and will inspire further studies.

[1]  Jürgen Kurths,et al.  Onymity promotes cooperation in social dilemma experiments , 2017, Science Advances.

[2]  Jun Tanimoto,et al.  Coevolution of discrete, mixed, and continuous strategy systems boosts in the spatial prisoner's dilemma and chicken games , 2017, Appl. Math. Comput..

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

[4]  Zhen Wang,et al.  Freezing period strongly impacts the emergence of a global consensus in the voter model , 2014, Scientific Reports.

[5]  Juan Wang,et al.  Evolution of cooperation in the spatial public goods game with adaptive reputation assortment , 2016 .

[6]  R. Trivers.  The Evolution of Reciprocal Altruism , 1971, The Quarterly Review of Biology.

[7]  Matjaž Perc,et al.  Evolutionary and dynamical coherence resonances in the pair approximated prisoner's dilemma game , 2006 .

[8]  M. Perc,et al.  Self-organization of punishment in structured populations , 2012, 1203.6900.

[9]  M. Perc,et al.  Promoting cooperation in social dilemmas via simple coevolutionary rules , 2008, 0812.1122.

[10]  Charles Darwin,et al.  On the origin of species, 1859 , 1988 .

[11]  M. Nowak,et al.  Evolutionary Dynamics of Biological Games , 2004, Science.

[12]  Chen Liu,et al.  Coevolution of multi-game resolves social dilemma in network population , 2019, Appl. Math. Comput..

[13]  P. Holme,et al.  Effects of strategy-migration direction and noise in the evolutionary spatial prisoner's dilemma. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Steve Miller,et al.  Population Fluctuation Promotes Cooperation in Networks , 2014, Scientific Reports.

[15]  G. Szabó,et al.  Phase diagrams for an evolutionary prisoner's dilemma game on two-dimensional lattices. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Cheng-Yi Xia,et al.  Role of Investment Heterogeneity in the Cooperation on Spatial Public Goods Game , 2014, PloS one.

[17]  M. Perc,et al.  Aspiration-based coevolution of link weight promotes cooperation in the spatial prisoner's dilemma game , 2018, Royal Society Open Science.

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

[19]  Wei Chen,et al.  Coevolution of aspirations and cooperation in spatial prisoner's dilemma game , 2015 .

[20]  Jun Tanimoto,et al.  Scaling the phase-planes of social dilemma strengths shows game-class changes in the five rules governing the evolution of cooperation , 2018, Royal Society Open Science.

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

[22]  M. Nowak,et al.  THE SPATIAL DILEMMAS OF EVOLUTION , 1993 .

[23]  Wei Wang,et al.  Evolution of cooperation on independent networks: The influence of asymmetric information sharing updating mechanism , 2019, Appl. Math. Comput..

[24]  H. Ohtsuki,et al.  Evolution of cooperation on adaptively weighted networks. , 2011, Journal of theoretical biology.

[25]  Attila Szolnoki,et al.  Probabilistic sharing solves the problem of costly punishment , 2014, ArXiv.

[26]  Attila Szolnoki,et al.  Coevolutionary Games - A Mini Review , 2009, Biosyst..

[27]  S. Kokubo,et al.  Insight into the so-called spatial reciprocity. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[29]  Huijia Li,et al.  Punishment diminishes the benefits of network reciprocity in social dilemma experiments , 2017, Proceedings of the National Academy of Sciences.

[30]  Zhen Wang,et al.  Spontaneous Symmetry Breaking in Interdependent Networked Game , 2014, Scientific Reports.

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

[32]  Jun Zhang,et al.  Evolution of cooperation among mobile agents with heterogenous view radii , 2011 .

[33]  Jun Tanimoto,et al.  How does resolution of strategy affect network reciprocity in spatial prisoner's dilemma games? , 2017, Appl. Math. Comput..

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

[35]  Leibo Liu,et al.  Stochastic Analysis of Multiplex Boolean Networks for Understanding Epidemic Propagation , 2018, IEEE Access.

[36]  G. Szabó,et al.  Cooperation enhanced by inhomogeneous activity of teaching for evolutionary Prisoner's Dilemma games , 2006, q-bio/0610001.

[37]  Zengqiang Chen,et al.  Risk Analysis and Enhancement of Cooperation Yielded by the Individual Reputation in the Spatial Public Goods Game , 2017, IEEE Systems Journal.

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

[39]  R. Glauber.  Time‐Dependent Statistics of the Ising Model , 1963 .

[40]  A. Barabasi,et al.  Evolution of the social network of scientific collaborations , 2001, cond-mat/0104162.

[41]  Juan Wang,et al.  Inferring the reputation enhances the cooperation in the public goods game on interdependent lattices , 2017, Appl. Math. Comput..

[42]  Attila Szolnoki,et al.  Coevolutionary success-driven multigames , 2014, ArXiv.

[43]  C. Hauert,et al.  Reputation-based partner choice promotes cooperation in social networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  Béla Bollobás,et al.  The degree sequence of a scale‐free random graph process , 2001, Random Struct. Algorithms.

[45]  Jun Tanimoto,et al.  Relationship between dilemma occurrence and the existence of a weakly dominant strategy in a two-player symmetric game , 2007, Biosyst..

[46]  D. Wilson.  Structured Demes and the Evolution of Group-Advantageous Traits , 1977, The American Naturalist.

[47]  M. Perc,et al.  Coevolution of teaching activity promotes cooperation , 2008, 0803.4091.

[48]  Shuai Ding,et al.  Evolution of cooperation in the traveler's dilemma game on two coupled lattices , 2014, Appl. Math. Comput..

[49]  J. Nash.  Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

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

[51]  Attila Szolnoki,et al.  Individual wealth-based selection supports cooperation in spatial public goods games , 2016, Scientific Reports.

[52]  Tong Li,et al.  Self-organized interdependence among populations promotes cooperation by means of coevolution. , 2019, Chaos.

[53]  Jun Tanimoto,et al.  Influence of bolstering network reciprocity in the evolutionary spatial Prisoner’s Dilemma game: a perspective , 2018, The European Physical Journal B.

[54]  György Szabó,et al.  Evolutionary prisoner's dilemma games with voluntary participation. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.