課程資訊
課程名稱
演化動力學
Evolutionary Dynamics 
開課學期
108-2 
授課對象
理學院  數學研究所  
授課教師
陳俊全 
課號
MATH5083 
課程識別碼
221 U8300 
班次
 
學分
3.0 
全/半年
半年 
必/選修
選修 
上課時間
星期三5,6,7(12:20~15:10) 
上課地點
天數305 
備註
總人數上限:30人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1082MATH5083_ED 
課程簡介影片
 
核心能力關聯
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課程概述

Evolution is a central theme in biology. Understanding evolution is also very important in the study of agricultural, medical, computer and social sciences. This course introduces the basic mathematical principles of evolutionary game theory and how cooperation emerges among selfish individuals. The contents cover the Nash equilibrium, evolutionarily stable strategy, social dilemmas of cooperation, effects of direct and indirect reciprocity, and models involving reputation.  

課程目標
待補 
課程要求
Course prerequisite: Linear algebra, calculus, ordinary differential equations. 
預期每週課後學習時數
 
Office Hours
 
參考書目
待補 
指定閱讀
Karl Sigmund: Calculus of Selfishness
Martin Nowak: Evolutionary Dynamics
Josef Hofbauer and Karl Sigmund: Evolutionary Games and Population Dynamics
 
評量方式
(僅供參考)
   
課程進度
週次
日期
單元主題
第3週
3/04  Introduction: evolution and (population) game theory; social life and animal behavior; brief history of game theory: von Neumann-Morgenstern; Nash; Maynard Smith 
第4週
3/11  Examples of simple games: Hawk-Dove game, Chicken game, a poker game, Rock-Scissors-Paper game, Prisoner's dilemma, Donation game
Rational thinking and choice: some examples
Pareto optimal, maximin strategy, Nash equilibrium 
第5週
3/18  1. Mixed-strategies, Nash equilibrium for a mixed-strategy game
2. Introduction on population dynamics  
第6週
3/25  1. Strictly dominant strategy, Pareto optimal, Nash equilibrium, strict Nash equilibrium
2. Replicator equations, imitation dynamics
3. Basic theory of 1st order ODE: existence, uniqueness, equilibrium, asymptotic behavior
4. Hawk-Dove game: pure-strategy Nash equilibrium, mixed-strategy Nash equilibrium, equilibria of the replicator equations and their stability  
第7週
4/01  1. Classification of the dynamical behavior of 2-species replicator system
2. Dynamics of a modified Rock-Scissors-Paper game, Lyapunov function 
第8週
4/08  1. Symmetric Nash equilibrium, relation between Nash equilibria and the equilibria of replicator equations
2. Symmetrization of a 2-player game
3. Brouwer's fixed point theorem 
第9週
4/15  1. Vector-field version of the Brouwer fixed point theorem
2. The Brouwer fixed point theorem on a simplex
3. Proof of the fixed theorem via the Sperner Lemma
4. Existence of Nash equilibria  
第10週
4/22  1. Sperner's lemma
2. Stochastic processes in finite populations, Moran's model 
第11週
4/29  Remarks on Sperner's lemma 
第12週
5/06  Evolutionarily Stable Strategy (ESS); An ESS is an asymptotically stable equilibrium of the replicator equations. 
第13週
5/13  Reciprocity: the role of repetition.
1. Repeated Prisoner's Dilemma
2. Backward induction; the shadow of the future
3. Axelrod's tournaments: TFT=Tit for Tat
4. Probability model: expected number of rounds, expected payoff 
第14週
5/20  1. Repeated donation game for AllC, AllD, and TFT
2. Replicator equations for AllC, AllD, and TFT; Nash equilibria; Lyapunov function 
第15週
5/27  1. The orbits and dynamics of the replicator equations for AllC, AllD, and TFT
2. Stochastic reactive strategies 
第16週
6/03  1. Linkage between the moves of players I and II
2. Recursive formulas for the cooperation levels
3. Expected payoff for player I against player II 
第17週
6/10  1. payoffs for reactive strategies
2. Replicator equations for AllC, AllD, and TFT with errors
3. Lyapunov function
 
第18週
6/17  1. Dynamics for AllC, AllD and TFT with errors
2. Dynamics on the space of reactive strategies: TFT and Generous TFT
3. Memory-one strategies: AllC, AllD, TFT, S2, S8, Pavlov 
第19週
6/24  1. Exercise
2. Simulation: https://audreyt.github.io/trust-zh-TW/