Evolutionary dynamics in division of labor games on cycle networks

Abstract This paper theoretically investigates the evolutionary dynamics in the division of labor games performed on the cycle networks. Several typical updating processes based on the Moran process are considered here: Birth-Death (BD) updating process, Death-Birth (DB) updating process and the mixed DB-BD updating process. The exponential payoff-to-fitness mapping is adopted, and analytical results for fixation time and fixation probability under the condition of strong selection are provided. In addition, numerical values of several crucial quantities within the framework of different game scenarios, decided by the payoff matrix of the division of labor (DOL) games, are studied for comparison. The conclusion clearly shows that, even under different kinds of DOL games, the fixation times are closely associated with the specific update mechanism. This work provides a deeper look into the strategic interactions and network dynamics in the context of the DOL games based on self-organized task allocation.

[1]  Martin A. Nowak,et al.  Evolutionary dynamics on graphs , 2005, Nature.

[2]  Ángel Sánchez,et al.  Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics , 2009, Physics of life reviews.

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

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

[5]  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.

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

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

[8]  Martin A Nowak,et al.  Evolutionary games on cycles , 2006, Proceedings of the Royal Society B: Biological Sciences.

[9]  Long Wang,et al.  Coevolving agent strategies and network topology for the public goods games , 2011 .

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

[11]  Thierry Burger-Helmchen,et al.  Division of labor and division of knowledge: A case study of innovation in the video game industry , 2009 .

[12]  M. Nowak,et al.  Evolutionary dynamics in structured populations , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

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

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

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

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

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

[18]  Xiang Li,et al.  Quantifying the contact memory in temporal human interactions , 2018, 2018 IEEE International Symposium on Circuits and Systems (ISCAS).

[19]  H. Ohtsuki,et al.  The replicator equation on graphs. , 2006, Journal of theoretical biology.

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

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

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

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

[24]  M. Nowak,et al.  Evolutionary games on cycles with strong selection. , 2017, Physical review. E.

[25]  Roberto Natalini,et al.  A hyperbolic model of spatial evolutionary game theory , 2011 .

[26]  C. Hauert,et al.  Punishment and reputation in spatial public goods games , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[27]  Jianlei Zhang,et al.  Fixation of competing strategies when interacting agents differ in the time scale of strategy updating. , 2016, Physical review. E.

[28]  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.

[29]  Jianlei Zhang,et al.  Crucial role of strategy updating for coexistence of strategies in interaction networks. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Martin A Nowak,et al.  The one-third law of evolutionary dynamics. , 2007, Journal of theoretical biology.

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

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

[33]  Chunyan Zhang,et al.  Punishment in the form of shared cost promotes altruism in the cooperative dilemma games. , 2017, Journal of theoretical biology.

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

[35]  Tianguang Chu,et al.  Does insurance against punishment undermine cooperation in the evolution of public goods games? , 2013, Journal of theoretical biology.

[36]  Michael Doebeli,et al.  Consolidating Birth-Death and Death-Birth Processes in Structured Populations , 2013, PloS one.

[37]  T. Chu,et al.  The evolution of cooperation in spatial groups , 2011 .

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

[39]  Arne Traulsen,et al.  The mechanics of stochastic slowdown in evolutionary games. , 2012, Journal of theoretical biology.

[40]  Edward O. Laumann,et al.  The Effect of Structural Embeddedness on the Division of Household Labor: A Game-Theoretic Model Using a Network Approach , 2003 .

[41]  X. Vives.  Nash equilibrium with strategic complementarities , 1990 .

[42]  Guangming Xie,et al.  Effects of encounter in a population of spatial prisoner's dilemma players. , 2011, Theoretical population biology.

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

[44]  Matjaz Perc,et al.  Grand Challenges in Social Physics: In Pursuit of Moral Behavior , 2018, Front. Phys..