%0 Journal Article %1 Graeser2011 %A Gräser, Oliver %A Xu, Chen %A Hui, P. M. %D 2011 %J New Journal of Physics %K adaptive-networks coevolution evolution game-theory graphs mean-field moment-closure networks pair-approximation snowdrift-game %N 8 %P 083015 %R 10.1088/1367-2630/13/8/083015 %T Analytic approach to co-evolving dynamics in complex networks: dissatisfied adaptive snowdrift game %V 13 %X We investigate the formulation of mean-field (MF) approaches for co-evolving dynamic model systems, focusing on the accuracy and validity of different schemes in closing MF equations. Within the context of a recently introduced co-evolutionary snowdrift game in which rational adaptive actions are driven by dissatisfaction in the payoff, we introduce a method to test the validity of closure schemes and analyse the shortcomings of previous schemes. A previous scheme suitable for adaptive epidemic models is shown to be invalid for the model studied here. A binomial-style closure scheme that significantly improves upon the previous schemes is introduced. Fixed-point analysis of the MF equations not only explains the numerical observed transition between a connected state with suppressed cooperation and a highly cooperative disconnected state, but also reveals a previously undetected connected state that exhibits the unusual behaviour of decreasing cooperation as the temptation for uncooperative action drops. We proposed a procedure for selecting proper initial conditions to realize the unusual state in numerical simulations. The effects of the mean number of connections that an agent carries are also studied.

@article{Graeser2011, abstract = {We investigate the formulation of mean-field ({MF}) approaches for co-evolving dynamic model systems, focusing on the accuracy and validity of different schemes in closing {MF} equations. Within the context of a recently introduced co-evolutionary snowdrift game in which rational adaptive actions are driven by dissatisfaction in the payoff, we introduce a method to test the validity of closure schemes and analyse the shortcomings of previous schemes. A previous scheme suitable for adaptive epidemic models is shown to be invalid for the model studied here. A binomial-style closure scheme that significantly improves upon the previous schemes is introduced. Fixed-point analysis of the {MF} equations not only explains the numerical observed transition between a connected state with suppressed cooperation and a highly cooperative disconnected state, but also reveals a previously undetected connected state that exhibits the unusual behaviour of decreasing cooperation as the temptation for uncooperative action drops. We proposed a procedure for selecting proper initial conditions to realize the unusual state in numerical simulations. The effects of the mean number of connections that an agent carries are also studied.}, added-at = {2011-08-15T10:10:52.000+0200}, author = {Gräser, Oliver and Xu, Chen and Hui, P. M.}, biburl = {https://www.bibsonomy.org/bibtex/2fb7a57b7b40b67d4348dc7f18b609419/rincedd}, doi = {10.1088/1367-2630/13/8/083015}, interhash = {f205c90ae2a67b0dc5421f59e9bd5558}, intrahash = {fb7a57b7b40b67d4348dc7f18b609419}, journal = {New Journal of Physics}, keywords = {adaptive-networks coevolution evolution game-theory graphs mean-field moment-closure networks pair-approximation snowdrift-game}, number = 8, pages = 083015, timestamp = {2011-08-15T10:10:53.000+0200}, title = {Analytic approach to co-evolving dynamics in complex networks: dissatisfied adaptive snowdrift game}, volume = 13, year = 2011 }