Title Page
Contents
Abstract 10
요약 12
Chapter Ⅰ. Introduction 14
Chapter Ⅱ. Evolutionary game theory 18
1. Two-player game and payoff 19
2. Prisoner's dilemma game 19
3. Iterated prisoner's dilemma game in a population 20
4. Evolutionary Stable Strategy 20
5. Imitation dynamics 21
6. Indirect reciprocity 22
Chapter Ⅲ. Win-Stay-Lose-Shift as a self-confirming equilibrium in the iterated Prisoner's Dilemma 24
1. Introduction 24
2. Method and Result 26
2.1. Best-response relations without observational uncertainty 26
2.2. Observational learning 31
3. Summary and Discussion 39
Chapter Ⅳ. Strategy inference using the maximum likelihood estimation in the iterated prisoner's dilemma game 43
1. INTRODUCTION 43
2. Methods 44
3. Results and discussion 50
3.1. m₁ vs m₁ 50
3.2. m₁ vs TFT-ATFT (m₂) 52
4. Summary and discussion 54
Chapter Ⅴ. Social norms in indirect reciprocity with ternary reputations 56
1. INTRODUCTION 56
2. Model 59
2.1. Description 59
2.2. Calculation 61
3. Methods 63
3.1. Calculation of the stationary-state population 63
3.2. Calculation of the cooperation level and the payoffs 65
3.3. Enumeration of norms 67
4. Results 67
4.1. Leading eight in the binary-reputation model 67
4.2. CESS's in the ternary-reputation model 70
4.3. Details of each type 73
4.4. Dynamics of C3 norms 75
5. Summary and Discussion 77
Chapter Ⅵ. Conclusions 81
Bibliography 83
Table Ⅱ-1. Best response among M₁ pure strategies. Against each strategy in the first column, we obtain the best response (the second column), and the resulting average payoff... 30
Table Ⅱ-2. Stationary probability distribution v(dγ, dγ, є), where we have retained only the leading-order term in the є-expansion for each vXY . When we describe a strategy in...[이미지참조] 32
Table Ⅱ-1. All of the deterministic m₁ strategies. d₀, d₅ -d₇, and d₁₅ are well-known strategies. d₀ (d₁₅) is a strategy that always cooperates (defects) regardless of the co-player's... 46
Table Ⅲ-2. 16 pairs of strategies if Alice uses d₀, and their corresponding stationary distributions. The distribution depends on є. By using the Taylor series when є ≈ 0,... 52
Table Ⅲ-3. Bob's strategy combining the Tit-for-tat and Anti-tit-for-tat (TA). TA prescribes the 16 actions because it considers the states of the two previous rounds. In this... 53
Table Ⅲ-4. The result of Alice's inference with an assumption that Bob's strategy is m₁ when his true strategy is TA (m₂), with N=10², L=10⁴,є=10¯². The first column... 54
Table Ⅳ-1. Prescriptions that are commonly shared by the leading eight. The asterisk (*) is a wildcard, meaning that it can be any of G and B. The left two columns show... 68
Figure Ⅱ-1. Graphical representation of best-response relations in Table II-1. If dμ is the best response to dν, we represent it as an arrow from dν to dμ. The blue node means...[이미지참조] 31
Figure Ⅱ-2. Best-looking responses to maximize the expected payoff under uncertainty in observation, when 1 ≪ M ≪ є¯¹. Compared with Fig. II-1, the first difference is that... 34
Figure Ⅱ-3. Effect of the prior on the observer's choice. A point in the triangle represents three fractions, which sum up to one, and its distance to an edge is proportional to... 38
Figure Ⅱ-1. Schematic diagram of Alice's inference process. (A) Alice uses a strategy di which is one of m₁ strategies. dj is hypothetical Bob's strategy that Alice assumes, and...[이미지참조] 49
Figure Ⅲ-2. The number of inaccurate inferences with each stationary state, α, β, γ, and δ. The x-axis of each graph is the observation length, L. Long-time observation... 51
Figure Ⅳ-1. Number of the CESS's for various values of b/c when μa=μe=10¯³ and pcth=0.99. CESS's are calculated for b/c=1.1, 1.5, 2, 3, . . ., 10. The horizontal...[이미지참조] 72
Figure Ⅳ-2. (a) Frequency of the stationary-state fractions hG* and hB*, respectively, for the core set. The vertical axis is on a logarithmic scale. (b) Scaling relations between...[이미지참조] 72