Evolutionary Snowdrift Game Incorporating Costly Punishment
The role of punishments in promoting cooperation is an important issue. We incorporate costly punishments into the snowdrift game (SG) by introducing a third punishing (P) character and study the effects. The punishers, who carry basically a cooperative (C) character, are willing to pay a...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IIUM Press, International Islamic University Malaysia
2012-01-01
|
| Series: | International Islamic University Malaysia Engineering Journal |
| Online Access: | http://journals.iium.edu.my/ejournal/index.php/iiumej/article/view/206 |
| Summary: | The role of punishments in promoting cooperation is an important issue. We incorporate costly punishments into the snowdrift game (SG) by introducing a third punishing (P) character and study the effects. The punishers, who carry basically a cooperative (C) character, are willing to pay a cost of a so as to punish a non-cooperative (D) opponent by ß. Depending on the initial fractions of the characters, a, ß, and the cost-to-benefit ratio r in SG, the three-character system evolves either into a steady state consisting only of C and P characters or only of C and D characters in a well-mixed population. The former situation represents an enhancement in cooperation relative to SG, while the latter is similar to SG. The dynamics in approaching these different steady states are found to be different. Analytically, the key features in the steady states and dynamics obtained by simulations are captured by a set of differential equations. The sensitivity to the initial distribution of characters is studied by depicting the flow in a phase portrait and analyzing the nature of fixed points. The analysis also shows the role of P-character in preventing a system from invasion by D-character agents. Starting from a population consisting only of C and P agents, a D-character agent intended to invade the system cannot survive when the initial fraction of P-agents is greater than r/ß. Our model, defined intentionally as a simulation algorithm, can be readily generalized to incorporate many interesting effects, such as those in a networked population. <br /><br /><strong>ABSTRAK</strong>: Peranan hukuman dalam meningkatkan kerjasama merupakan isu penting. Hukuman berat diterapkan ke dalam permainan hanyutan salji (snowdrift game (SG)) dengan memperkenalkan karekter penghukum (P) ketiga dan akibatnya dipantau. Penghukum, pada asasnya membawa watak koperatif (C), sanggup membayar kos a, agar dia menghukum lawan yang tidak koperatif (D) dengan ß. Bergantung kepada pecahan permulaan watak-watak, a, ß, dan nisbah faedah-kos r dalam SG, sistem tiga watak ini berkembang sama ada kepada keadaan mantap yang hanya terdiri daripada karekter C dan P atau hanya karekter C dan D dalam populasi gabungan sempurna. Situasi sebelumnya mempamerkan peningkatan dalam kerjasama berkaitan dengan SG, manakala yang sebelumnya mirip dengan SG. Dinamik dalam mendapatkan pelbagai keadaan mantap didapati adalah berbeza. Secara terperincinya, kunci utama dalam keadaan mantap dan dinamik diperolehi melalui simulasi yang diperolehi daripada satu set persamaan perbezaan. Kepekaan terhadap permulaan pembahagian watak dikaji dengan menggambarkan aliran dalam portrait fasa dan menganalisa sifat titik-titik tetap. Analisa juga menggambarkan fungsi karekter-P dalam menghalang suatu sistem daripada dicerobohi agen karekter-D. Bermula dengan satu populasi yang hanya terdiri daripada agen C & D, karekter-D bertujuan menyerang sistem yang tidak mampu bertahan apabila pecahan permulaan agen P melebihi r/ß. Model, didefinisikan sebagai algoritma simulasi, boleh secara amnya menggabungkan banyak aspek menarik, seperti di dalam populasi rangkaian.<br /><br />KEYWORDS: evolutionary; snowdrift game; well-mixed population<br /><br /> |
|---|---|
| ISSN: | 1511-788X 2289-7860 |