ESSAYS ON NON-COOPERATIVE INVENTORY GAMES

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ESSAYS ON NON-COOPERATIVE INVENTORY
GAMES
Evren K¨orpeo˘glu
Ph.D. in Industrial Engineering
Supervisor: Assist. Prof. Dr. Alper S¸en
January, 2012
Contents
1 INTRODUCTION 1
2 GAME THEORY REVIEW 9
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Definition of a game . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Mixed Strategies . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.2 Dominated Strategies . . . . . . . . . . . . . . . . . . . . . 10
2.2.3 Best Response functions . . . . . . . . . . . . . . . . . . . 11
2.2.4 Nash Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.5 Extensive Form Games . . . . . . . . . . . . . . . . . . . . 13
2.3 Bayesian Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1 Bayesian Nash Equilibrium . . . . . . . . . . . . . . . . . 15
2.4 Mechanism Design . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Game Theory Applications . . . . . . . . . . . . . . . . . . . . . . 16
3 A PRIVATE CONTRIBUTIONS GAME FOR JOINT REPLENISHMENT   18
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 The Model and Preliminaries . . . . . . . . . . . . . . . . . . . . 22
3.2.1 Independent (decentralized) replenishment . . . . . . . . . 23
3.2.2 Centralized joint replenishment . . . . . . . . . . . . . . . 24
3.2.3 MGB: a direct mechanism for joint replenishment . . . . . 24
3.3 One–Stage private contributions game for joint replenishment . . 26
3.4 Two-stage private contributions game for joint replenishment . . . 33
3.4.1 Stage 2: Equilibrium contributions in subgame g(δ,M) . . 34 ESSAYS ON NON-COOPERATIVE INVENTORYGAMES.pdf (801.78 KB, 需要: 1 个论坛币)

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3.4.2 Stage 1: Equilibrium participation . . . . . . . . . . . . . 35
3.4.3 Subgame–Perfect Equilibria . . . . . . . . . . . . . . . . . 36
3.5 Comparison of cycle times and aggregate costs . . . . . . . . . . . 38
3.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 40
4 PRIVATE CONTRIBUTIONS GAME WITH ASYMMETRIC
INFORMATION 42
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3 Asymmetric Information . . . . . . . . . . . . . . . . . . . . . . . 45
4.4 Numerical Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 56
5 A THREE-STAGE GAME FOR JOINT REPLENISHMENT
WITH PRIVATE CONTRIBUTIONS 59
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2 The Model and Preliminaries . . . . . . . . . . . . . . . . . . . . 60
5.2.1 Stage 3: Participation . . . . . . . . . . . . . . . . . . . . 62
5.2.2 Stage 2: RSP’s cycle time decision . . . . . . . . . . . . . 63
5.2.3 Stage 1: Private Contribution . . . . . . . . . . . . . . . . 64
5.2.4 Subgame–Perfect Equilibrium . . . . . . . . . . . . . . . . 64
5.3 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 68
6 DESIGN AND ANALYSIS OF MECHANISMS FOR DECENTRALIZED
JOINT REPLENISHMENT 69
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2 The Model and Preliminaries . . . . . . . . . . . . . . . . . . . . 71
6.2.1 Independent (decentralized) replenishment . . . . . . . . . 72
6.2.2 Centralized joint replenishment . . . . . . . . . . . . . . . 72
6.3 Direct Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.4 Two–Parameter Mechanisms . . . . . . . . . . . . . . . . . . . . . 75
6.5 One–Parameter Mechanisms . . . . . . . . . . . . . . . . . . . . . 79
6.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 88
7 NEWSBOY DUOPOLY WITH ASYMMETRIC INFORMATION
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.3 A Model of Newsboy Duopoly . . . . . . . . . . . . . . . . . . . . 95
7.3.1 Industry and Firm Demands . . . . . . . . . . . . . . . . . 95
7.3.2 Cost and Information Structures . . . . . . . . . . . . . . 97
7.3.3 Actions, Strategies and Payoffs . . . . . . . . . . . . . . . 97
7.4 Equilibrium Order Quantities . . . . . . . . . . . . . . . . . . . . 98
7.4.1 Equilibrium Existence . . . . . . . . . . . . . . . . . . . . 99
7.4.2 Preliminary Observations on the Equilibrium . . . . . . . . 100
7.4.3 Structure of the Equilibrium . . . . . . . . . . . . . . . . . 103
7.4.4 Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . 106
7.4.5 Intra–equilibrium Comparisons . . . . . . . . . . . . . . . 109
7.4.6 Comparative Statics . . . . . . . . . . . . . . . . . . . . . 109
7.5 A Special Case: Uniform Demand and Linear Market Shares . . . 111
7.5.1 A Partition of the Parameter Space . . . . . . . . . . . . . 111
7.5.2 Equilibrium Order Quantities . . . . . . . . . . . . . . . . 113
7.5.3 Equilibrium Payoffs . . . . . . . . . . . . . . . . . . . . . . 114
7.5.4 Comparative Statics . . . . . . . . . . . . . . . . . . . . . 115
7.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 116
8 CONCLUSIONS 117
APPENDIX 120

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