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The interaction energy of charged filaments in an electrolyte: Results for all filament spacings |
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| Authors: | Smith D A |
| Institution: | a Department of Mathematical Engineering and Information Physics, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan b PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan c Department of Value and Decision Science, Tokyo Institute of Technology, 2-12-1-W9-35 O-okayama, Meguro, Tokyo 152-8552, Japan |
| Abstract: | Recent studies have explored interactions between evolutionary game dynamics and population structure. Yet most studies so far mainly paid attention to unweighted and static networks. Here we explore evolutionary games played on dynamically weighted networks. Players update their strategies according to the payoffs they obtain. Players also update weights of their adjacent links depending on payoffs they gain through those links; profitable links are reinforced whereas unprofitable ones are weakened. The system is characterized by two time scales, the one for strategy update, βS, and the other for weight adjustment, βW. We find that, under a mean-field approximation, the asymptotic behavior of the system is described by the replicator equation with an effective payoff matrix, which is a combination of the original game matrix A and its transpose, AT. Both analytical and numerical results show that such an adaptive weight adjustment mechanism dramatically promotes evolution of cooperation. |
| Keywords: | Evolutionary game theory Payoff matrix Dynamical network Partner choice |
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