An Introduction to Dynamic Games_A. Haurie & J. Krawczyk_March 28, 2000

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【文库PDF格式】An Introduction to Dynamic Games_A. Haurie & J. Krawczyk_March 28, 2000

应该有人感兴趣。。百度文库20分。。




Contents
1 Foreword                             9
2 Decision Analysis with Many Agents 15
2.1 The Basic Concepts of Game Theory . . . . . . . . . . . . . . . . . . 15
2.2 Games in Extensive Form . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Additional concepts about information . . . . . . . . . . . . . . . . . 20
2.4 Games in Normal Form . . . . . . . . . . . . . . . . . . . . . . . . 21
3 Solution concepts for noncooperative games 27
3.1 introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Matrix Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 Bimatrix Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4 Concave m-Person Games . . . . . . . . . . . . . . . . . . . . . . . 44
3.5 Cournot equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.6 Correlated equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.7 Bayesian equilibrium with incomplete information . . . . . . . . . . 60
3.8 Appendix on Kakutani Fixed-point theorem . . . . . . . . . . . . . . 64
3.9 exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
II Repeated and sequential Games 67
4 Repeated games and memory strategies 69
4.1 Repeating a game in normal form . . . . . . . . . . . . . . . . . . . 70
4.2 Folk theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3 Collusive equilibrium in a repeated Cournot game . . . . . . . . . . . 77
4.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5 Shapley’s Zero Sum Markov Game 83
5.1 Process and rewards dynamics . . . . . . . . . . . . . . . . . . . . . 83
5.2 Information structure and strategies . . . . . . . . . . . . . . . . . . 84
5.3 Shapley’s-Denardo operator formalism . . . . . . . . . . . . . . . . . 86
6 Nonzero-sum Markov and Sequential games 89
6.1 Sequential Game with Discrete state and action sets . . . . . . . . . . 89
6.2 Sequential Games on Borel Spaces . . . . . . . . . . . . . . . . . . . 92
6.3 Application to a Stochastic Duopoloy Model . . . . . . . . . . . . . . 93
III Differential games 99
7 Controlled dynamical systems 101
7.1 A capital accumulation process . . . . . . . . . . . . . . . . . . . . . 101
7.2 State equations for controlled dynamical systems . . . . . . . . . . . 102
7.3 Feedback control and the stability issue . . . . . . . . . . . . . . . . 103
7.4 Optimal control problems . . . . . . . . . . . . . . . . . . . . . . . . 104
7.5 A model of optimal capital accumulation . . . . . . . . . . . . . . . . 104
7.6 The optimal control paradigm . . . . . . . . . . . . . . . . . . . . . 105
7.7 The Euler equations and the Maximum principle . . . . . . . . . . . . 106
7.8 An economic interpretation of the Maximum Principle . . . . . . . . 108
7.9 Synthesis of the optimal control . . . . . . . . . . . . . . . . . . . . 109
7.10 Dynamic programming and the optimal feedback control . . . . . . . 109
7.11 Competitive dynamical systems . . . . . . . . . . . . . . . . . . . . 110
7.12 Competition through capital accumulation . . . . . . . . . . . . . . . 110
7.13 Open-loop differential games . . . . . . . . . . . . . . . . . . . . . . 110
7.13.1 Open-loop information structure . . . . . . . . . . . . . . . . 110
7.13.2 An equilibrium principle . . . . . . . . . . . . . . . . . . . . 110
7.14 Feedback differential games . . . . . . . . . . . . . . . . . . . . . . 111
7.15 Why are feedback Nash equilibria outcomes different from Open-loop
Nash outcomes? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7.16 The subgame perfectness issue . . . . . . . . . . . . . . . . . . . . . 111
7.17 Memory differential games . . . . . . . . . . . . . . . . . . . . . . . 111
7.18 Characterizing all the possible equilibria . . . . . . . . . . . . . . . . 111
IV A Differential Game Model 113
7.19 A Game of R&D Investment . . . . . . . . . . . . . . . . . . . . . . 115
7.19.1 Dynamics of R&D competition . . . . . . . . . . . . . . . . 115
7.19.2 Product Differentiation . . . . . . . . . . . . . . . . . . . . . 116
7.19.3 Economics of innovation . . . . . . . . . . . . . . . . . . . . 117
7.20 Information structure . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.20.1 State variables . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.20.2 Piecewise open-loop game. . . . . . . . . . . . . . . . . . . . 118
7.20.3 A Sequential Game Reformulation . . . . . . . . . . . . . . . 118

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