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Genetic algorithm and non-ESS solutions to game theory models

在遊戲理論中的遺傳演算法和非演化穩定策略解. Genetic algorithm and non-ESS solutions to game theory models. Animal Behaviour (2006). Steven Hamblin & Peter L. Hurd. presenter ： Yi-Chung Wang ( 王 浥 璋 ) 生四乙 498432037. Introduction. 基因演算法 Genetic Algorithms (GA). Introduction. 基因演算法 Genetic Algorithms (GA).

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Genetic algorithm and non-ESS solutions to game theory models

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  1. 在遊戲理論中的遺傳演算法和非演化穩定策略解在遊戲理論中的遺傳演算法和非演化穩定策略解 Genetic algorithm and non-ESS solutions to game theory models Animal Behaviour (2006) Steven Hamblin & Peter L. Hurd presenter：Yi-Chung Wang (王浥璋) 生四乙 498432037

  2. Introduction 基因演算法Genetic Algorithms (GA)

  3. Introduction 基因演算法Genetic Algorithms (GA) 定義基因組以及適配函數，創造第一代的基因組 藉由選擇、雜交、以及突變，來修訂起始群體 重複步驟2，直到這個群體不再進步為止

  4. Introduction

  5. Introduction 搜尋終止 • 當搜尋到指定的代數時。 • 當搜尋結果達到所要求的目標時。 • 當搜尋結果停滯不前或已經達到某種飽和現象時。

  6. Introduction Evolutionary game theory(EGT)鷹-鴿策略(John Maynard Smith and George R. Price's)

  7. Introduction Evolutionary stable stratage(ESS) 囚犯的困境 （Prisoner's Dilemma） Nash Equilibrium

  8. Introduction Conventional signalling game • 只知道自己的狀態(強壯或瘦弱) ， 不知道別人的。 2. 隨機選擇A或B當做信號發出。 3. 在知道自己的狀態和對手發出的信號下，做出一種行為表現：攻擊(Attackt)、停止攻擊(Pause-Attack)、逃跑(Flee)) 4. 根據自身狀態和行為表現，計算得失。

  9. Reserch question ESS在Conventional signalling game中可能不是最佳的解，利用遺傳演算法尋找可能的最佳解。

  10. M & M 基因編碼 Strong (A) Weak (B) A A B B

  11. M & M 帶入參數 • TCNP(T =1.0, C =0.7, N =0.4, and P =0.1.) (Hurd & Enquist 1998) 2.VCDF(V =100, C1=15, C0=15,C1=70, FA=5,FP=5) (Hurd 1997)

  12. Results ESS Non-ESS Non-ESS ESS

  13. Results

  14. Conclution 1. 由結果顯示，ESS在初始族群的表現雖然不錯，但結果不是最主要的使用策略類型。 2.Non-ESS 的策略反而在300代後明顯被固定下來。

  15. Discussion • ESS在此model中可能根本不存在。 2. 演算法僅提供可能的解釋，並不一定符合真實狀況。

  16. Reference • Balkenborg, D. & Schlag, K. H. 2001. Evolutionary stable sets. International • Journal of Game Theory, 29, 571e595. • Enquist, M. 1985. Communication during aggressive interactionswith particular reference to variation in choice of behaviour. AnimalBehaviour, 33, 1152e1161. • Hurd, P. L. 1997. Is signalling of fighting ability costlier for weakerindividuals?Journal of Theoretical Biology, 184, 83e88. • Hurd, P. L. 2004. Conventional displays: evidence for socially mediated costs of threat displays in a lizard. Aggressive Behavior, 30,326e341. • Hurd, P. L. 2006. Resource holding potential, subjective resourcevalue and game theoretical models of aggressive signalling.Journal of Theoretical Biology, 241, 639e648. • Hurd, P. L. & Enquist, M. 1998. Conventional signalling in aggressive interactions: the importance of temporal structure. Journal ofTheoretical Biology, 192, 197e211. • Hurd, P. L. & Enquist, P. L. 2001. Threat display in birds. CanadianJournal of Zoology, 79, 931e942. • Orzack, S. H. & Hines, W. G. S. 2005. The evolution of strategy variation: will an ESS evolve? Evolution, 59, 1183e1193. • Szamado ´, S. 2000. Cheating as a mixed strategy in a simplemodel of aggressive communication. Animal Behaviour, 59,221e230. • Szamado ´, S. 2003. Threat displays are not handicaps. Journal of Theoretical Biology, 221, 327e348.

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