Stochastic dynamics of division of labor games in finite populations

Abstract A theoretical investigation on the strategy evolution in the self-organized division of labor dilemma is performed by means of evolutionary game theory. The often-used Fermi function is employed for driving the strategy updating, based on which the fixation probability of the involved strategy (performing which task) is calculated. Results about the evolution dynamics of the division of labor for two-player games are: (1) the fixation probabilityfor any selection intensity is derived; (2) the fixation probability and fixation time under weak selection are gained and a comparison with neutral selection is performed. In this case, the conditions to facilitate cooperation in division of labor are found. Then we extend the model to a multi-player one to describe the self-organized task allocation when multiple players are involved in one game. Relevant results for weak selection to favor the coexistence state of the two strategies for the multi-player games are gained. These results help understand and design effective mechanism where self-organized collective dynamics occurs in the form of maximizing the benefit of the multi-agent system.

[1]  D. Fudenberg,et al.  Emergence of cooperation and evolutionary stability in finite populations , 2004, Nature.

[2]  T. Antal,et al.  Fixation of Strategies for an Evolutionary Game in Finite Populations , 2005, Bulletin of mathematical biology.

[3]  J. Szép,et al.  Two-person games , 1985 .

[4]  Anita Raja,et al.  Emergence of Cooperation Using Commitments and Complex Network Dynamics , 2013, 2013 IEEE/WIC/ACM International Joint Conferences on Web Intelligence (WI) and Intelligent Agent Technologies (IAT).

[5]  M. Nowak,et al.  Stochastic dynamics of invasion and fixation. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Chunyan Zhang,et al.  Fixation of strategies driven by switching probabilities in evolutionary games , 2016 .

[7]  C. Hauert,et al.  Coevolutionary dynamics: from finite to infinite populations. , 2004, Physical review letters.

[8]  G. Robinson.  Regulation of division of labor in insect societies. , 1992, Annual review of entomology.

[9]  Gerhard Weiss,et al.  Evolution of cooperation in arbitrary complex networks , 2014, AAMAS.

[10]  M. Nowak,et al.  Evolutionary game dynamics in a Wright-Fisher process , 2006, Journal of mathematical biology.

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

[12]  Jun Tanimoto,et al.  A social dilemma structure in diffusible public goods , 2016 .

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

[14]  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.

[15]  Tianguang Chu,et al.  Cooperation enhanced by the 'survival of the fittest' rule in prisoner's dilemma games on complex networks. , 2010, Journal of theoretical biology.

[16]  H. Peyton Young,et al.  Stochastic Evolutionary Game Dynamics , 1990 .

[17]  Jinhu Lu,et al.  Towards A Theoretical Framework for Analysis and Intervention of Random Drift on General Networks , 2015, IEEE Transactions on Automatic Control.

[18]  Francisco C. Santos,et al.  The emergence of commitments and cooperation , 2012, AAMAS.

[19]  K. J. Ray Liu,et al.  Distributed Adaptive Networks: A Graphical Evolutionary Game-Theoretic View , 2012, IEEE Transactions on Signal Processing.

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

[21]  Adam Wierman,et al.  An architectural view of game theoretic control , 2011, SIGMETRICS Perform. Evaluation Rev..

[22]  Tom Lenaerts,et al.  Evolution of commitment and level of participation in public goods games , 2017, Autonomous Agents and Multi-Agent Systems.

[23]  Manh Hong Duong,et al.  On the Expected Number of Equilibria in a Multi-player Multi-strategy Evolutionary Game , 2014, Dynamic Games and Applications.

[24]  L. Keller,et al.  An Evolutionary Perspective on Self-Organized Division of Labor in Social Insects , 2011 .

[25]  Cheng-Yi Xia,et al.  Cooperation and strategy coexistence in a tag-based multi-agent system with contingent mobility , 2016, Knowl. Based Syst..

[26]  Attila Szolnoki,et al.  Statistical Physics of Human Cooperation , 2017, ArXiv.

[27]  Ming Cao,et al.  How insurance affects altruistic provision in threshold public goods games , 2015, Scientific Reports.

[28]  Drew Fudenberg,et al.  Evolutionary game dynamics in finite populations , 2004, Bulletin of mathematical biology.

[29]  I. Karsai,et al.  Productivity, individual-level and colony-level flexibility, and organization of work as consequences of colony size. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[30]  Nikos Nikiforakis,et al.  Altruistic punishment does not increase with the severity of norm violations in the field , 2016, Nature Communications.

[31]  Jianlei Zhang,et al.  Group penalty on the evolution of cooperation in spatial public goods games , 2010 .

[32]  R. Selten.  Evolutionary stability in extensive two-person games , 1983 .

[33]  E. Wilson,et al.  Caste and ecology in the social insects. , 1979, Monographs in population biology.

[34]  Chunlin Li,et al.  Collaborative content dissemination based on game theory in multimedia cloud , 2017, Knowl. Based Syst..

[35]  Manh Hong Duong,et al.  Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games , 2015, Journal of mathematical biology.

[36]  Ming Cao,et al.  Networks of conforming or nonconforming individuals tend to reach satisfactory decisions , 2016, Proceedings of the National Academy of Sciences.

[37]  M. Perc.  Coherence resonance in a spatial prisoner's dilemma game , 2006 .

[38]  Nigel R. Franks,et al.  Task allocation in ant colonies within variable environments (A study of temporal polyethism: Experimental) , 1993 .

[39]  Matjaž Perc,et al.  Phase transitions in models of human cooperation , 2016 .

[40]  Liu Xian-ning.  Fixation Probabilities in Evolutionary Dynamics with a Wright-Fisher Process in Finite Diploid Populations , 2011 .

[41]  M. Perc,et al.  Social diversity and promotion of cooperation in the spatial prisoner's dilemma game. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[43]  Tom Lenaerts,et al.  Centralized versus Personalized Commitments and Their Influence on Cooperation in Group Interactions , 2017, AAAI.

[44]  Martin A Nowak,et al.  Multi-player games on the cycle. , 2012, Journal of theoretical biology.

[45]  Arne Traulsen,et al.  Pairwise comparison and selection temperature in evolutionary game dynamics. , 2007, Journal of theoretical biology.

[46]  Georges Zaccour,et al.  Feedback Nash Equilibria in Linear-Quadratic Difference Games With Constraints , 2014, IEEE Transactions on Automatic Control.

[47]  Harry Eugene Stanley,et al.  The cost of attack in competing networks , 2015, Journal of The Royal Society Interface.

[48]  Debraj Ray.  A Game-Theoretic Perspective on Coalition Formation , 2007 .

[49]  Javier M. Buldú,et al.  Competition among networks highlights the power of the weak , 2016, Nature Communications.

[50]  Jaak Jurison,et al.  Productivity , 2002, Encyclopedia of Information Systems.

[51]  B. Stengel,et al.  COMPUTING EQUILIBRIA FOR TWO-PERSON GAMES , 1996 .

[52]  Feng Xia,et al.  A Signaling Game for Uncertain Data Delivery in Selfish Mobile Social Networks , 2016, IEEE Transactions on Computational Social Systems.

[53]  Long Wang,et al.  Evolutionary dynamics on graphs: Efficient method for weak selection. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  Hugh H. T. Liu,et al.  Game-Theoretical Persistent Tracking of a Moving Target Using a Unicycle-Type Mobile Vehicle , 2014, IEEE Transactions on Industrial Electronics.

[55]  R. Axelrod.  Effective Choice in the Prisoner's Dilemma , 1980 .

[56]  A. Traulsen,et al.  Fixation times in evolutionary games under weak selection , 2008, 0812.0851.

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

[58]  Arne Traulsen,et al.  The different limits of weak selection and the evolutionary dynamics of finite populations. , 2007, Journal of theoretical biology.