에이전트 선호 다양성을 반영한 이산 선택 게임 모형

Abstract

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 산업공학과, 2018. 8. 홍성필.We consider a discrete choice game model in which the agent's disutility is determined only by how the numbers of agents' choices are distributed over them. Its equilibrium is defined in the aggregate choices of agents so that taste heterogeneity is modeled through randomized parameters. This enables us to estimate the joint density of parameters from a collective choice data. The joint density is estimated by a biquadratic inverse optimization that matches observed choices to the equilibrium condition expressed in a set-valued best-response function. The model is capacitated with an arbitrary disutility function continuous in attributes and measurable in taste parameters. We observed that the proposed equilibrium defined as an aggregate choice of agents with such a disutility is actually equivalent to nonatomic Nash equilibrium defined in agent-specific variational inequality. In a comparison test on a massive metro route choice data, we demonstrate the proposed model is a good alternative to existing non-game choice models. An extended test also instantiates the advantage of the general disutility capable of formulating application-dependent choice behaviors of agents.Abstract i Contents v List of Tables vi List of Figures viii Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Objectives and contributions 6 1.3 Organization 8 Chapter 2 Preliminaries 10 2.1 Normal-form game 11 2.1.1 Nash equilibria 11 2.1.2 Related problems 16 2.2 Nonatomic congestion game 19 2.2.1 Wardrop equilibria 19 2.2.2 Equilibrium computation 25 2.2.3 Relation with variational inequality problem 26 2.3 Nonatomic congestion game with agents' heterogeneity 27 2.3.1 Multi-class models 28 2.3.2 Randomized VOT models 32 2.3.3 Equilibrium computation 33 2.4 Nonatomic game 35 2.4.1 Nonatomic Nash equilibria 36 2.4.2 Nonatomic externality game 37 2.5 Taste parameter estimation via discrete choice models 40 Chapter 3 P-equilibrium Model 44 3.1 Relationship with previous works 44 3.2 P-equilibria 45 3.3 Existence 52 3.4 Equivalence to a nonatomic Nash equilibrium 54 Chapter 4 Taste Parameter Estimation via Inverse Optimization 56 4.1 Inverse optimization 56 4.2 Inverse optimization for P-equilibrium model 57 4.3 Solving biquadratic program 61 4.4 Simple example in routing game 64 Chapter 5 Empirical Experiment 69 5.1 Metro route choice model in Seoul metropolitan area 69 5.1.1 Behaviors of metro passengers 69 5.1.2 Route choice sets 71 5.1.3 Attributes 71 5.2 Game vs nongame models for predicting metro route choices 73 5.2.1 P-equilibrium route choice model 73 5.2.2 Nongame route choice model 74 5.2.3 Performance evaluation 76 5.3 Modeling application-dependent choice behavior 80 5.3.1 CES-disutility for metro route choice 81 5.3.2 Performance evaluation 83 5.3.3 Biquadratic program computation results 84 Chapter 6 Conclusion and Future Work 87 6.1 Conclusion 87 6.2 Discussion and future work 88 Appendix 89 Bibliography 90 국문초록 108Docto