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.
%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
}