摘要
路径选择是出行行为研究领域的一个关键问题,它为许多交通问题研究提供了理论基础。传统路径选择问题研究通常假定出行者是完全理性的,其出行决策遵循期望效用理论,以出行的阻抗最小、效用或可靠性最大作为决策依据,较少考虑出行者的有限理性问题。本文围绕出行者的路径选择问题,在有限理性框架下基于前景理论进行出行行为分析和建模,研究出行者的动态路径选择行为与交通系统宏观运行状况之间的相互作用规律,探讨序贯出行决策中参照点的动态更新规律。
首先,分别对路径选择问题的研究现状和前景理论在出行行为研究中的应用进行了回顾和总结,指出了现状研究存在的问题和不足,进而提出论文的研究内容和技术路线;在此基础上对前景理论在出行行为研究中的适用性进行了探讨,研究认为前景是否适用于出行行为研究,关键要看出行者所考虑的选择方案属性是否具有不确定性,这一结论为前景理论在出行行为研究中的具体应用提供了指导和依据;此外,针对前景理论自身存在的局限,对在具体研究中如何选取更为合适的理论给出了建议。
第二,考虑交通网络行程时间的不确定性和出行者的感知误差,并基于行程时间可靠性和出行时间预算来设定出行路径选择的内生参照点,基于累积前景理论建立了一个随机用户均衡模型;分别在固定需求和弹性需求条件给出了等价的变分不等式,设计了求解算法并通过算例对模型及算法的有效性进行了验证;结合参数敏感性分析研究了参照点、风险偏好、损失规避和感知误差等出行者的认知和心理因素与网络均衡交通流之间的相互影响和相互作用规律。模型更加符合现实中出行者的决策行为特征,提高了交通需求预测的精确性。
第三,进一步考虑出发时间选择问题进行动态交通分配建模,以早高峰工作出行为研究对象,合理设定了出发时间和出行路径同时选择问题的参照点,基于累积前景理论建立了一个随机动态用户最优模型;给出了等价的变分不等式,设计了求解算法并通过算例分析了出行者的动态路径选择行为与时变的交通流之间的关系;在此基础上建立了动态可靠性指标来评价交通网络的运行效率和服务水平,并基于算例结果展现了出发时间选择与到达可靠性之间的关系。模型较好的克服了传统出发时间选择模型基于完全理性假设,以及“时间窗”和“计划延误成本”概念的局限。
第四,在不同信息提供条件下分别基于复制子动态、最优反应动态、Smith动态和BNN动态来考察出行者日常路径选择的博弈学习行为,基于累积前景理论建立了四个动态交通系统模型;分别在不同的初始状态和参照点更新规则下通过算例对交通流的动态演化与用户均衡的实现过程进行了数值模拟。均衡和演化两种分析方法的综合运用,揭示了交通流演化的内在动力机制,以及网络均衡的实现过程和条件,在有限理性框架下丰富和发展了传统的交通分配理论体系。
最后,将累积前景理论与贝叶斯法则相结合,构建了一个序贯出行决策学习模型,深入分析了序贯出行决策的特征和参照点的内涵及其影响因素,设计了一个路径选择实验,基于实验数据探讨了序贯出行决策中参照点的动态更新规律。实验研究方法的引入不仅为出行者行为的实证研究提供了思路和借鉴,也为前景理论在交通领域的实际应用创造了条件。
本文采用规范研究和实证分析相结合的方法,运用行为科学理论解析出行行为发生的微观机理,基于合理的行为假定和研究方法进行出行行为分析和建模,拓展了传统路径选择问题的研究思路,有关模型、算法和结论可以为交通分配、动态诱导、拥挤收费、区域限行等问题的研究提供理论依据。
Route choice is a key problem in travel behavior research field, which providestheoretical foundations for the research of many other traffic issues. Existing routechoice research is generally based on the assumption that travelers are entirelyrational and usually make their decisions based on minimum disutility, maximumutility or reliability of the available alternatives, and seldom considers travelers’bounded rationality in their decision-makings. Around the issue of route choice, thispaper is intended to analyze and model travel behavior based on Prospect Theorywithin the frame of bounded rationality. The interaction laws between travelers’dynamic route choice behavior and traffic system’s macroscopic operationalperformances are also investigated. Reference points’ updating rules in sequentialtravel decision scenes are explored as well.
Firstly, the state-of-art of route choice research and Prospect Theory’sapplication in travel behavior research is reviewed and summarized. Severalproblems and shortages in existing research are pointed out, followed by the maincontents and technical roadmap of the dissertation. Then around the applicability ofProspect Theory in travel behavior research, it is suggested that the key criterion liein whether the alternative attribute within traveler’s consideration involvesuncertainty or not. This conclusion provides guidance and foundation for the specificapplication of Prospect Theory in travel behavior research. In addition, some adviceon how to select a more suitable theory in actual research is given to avoid of severalexisting defects of Prospect Theory.
Secondly, in consideration of the uncertainty of travel time and travelers’perception errors in traffic network simultaneously, a Stochastic User Equilibriummodel based on Cumulative Prospect Theory is formulated, in which travelers’endogenous reference points are set by an integration of travel time reliability andtravel time budget. Then the equivalent variational inequalities and algorithms forthe model are given accordingly under the condition of fixed and elastic traveldemand, followed by two numerical examples respectively to provide validity of the model and algorithms. By parameter sensitivity analysis, a study of the interactionlaws between travelers’ cognitive and psychological factors, such as reference point,risk appetite, loss aversion and perception errors, and the traffic network equilibriumis then conducted. Conforming more to travelers’ decision behavior in reality, thesuggested model can improve the accuracy of traffic demand forecasting.
Thirdly, in order to apply Prospect Theory to dynamic traffic assignment inconsideration of the problem of departure time choice, a Stochastic Dynamic UserOptimum model based on Cumulative Prospect Theory is formulated, whichproperly handles the reference points of departure time and route choices focusingon commute trips in morning peak. After an equivalent variational inequality andalgorithm of the model are given, the influence of travelers’ dynamic route choicebehavior on time-varying traffic flow is analyzed through a numerical example. Thena set of dynamic travel reliability indicators are established for the purpose ofevaluating traffic network’s operational performance and service efficiency. Anillustration of the relationship between departure time choice and arrival reliabilitybased on the proposed numerical example is followed. The proposed model expandsthe concept of time-window and schedule delay well and overcomes the limitation ofentire rationality assumption in existing models dealing with departure time choice.
Fourthly, in scenarios of different information provision, four dynamical trafficsystem models are formulated based on Cumulative Prospect Theory, in which fourevolutionary dynamics, namely the replicator, the best response, the Smith and theBNN dynamics, are introduced to investigate travelers’ day-to-day route choicegame learning behavior respectively. Then the dynamical traffic flow evolution andachievements of User Equilibrium are presented through two numerical examplesunder different initial states and distinct reference points’ updating rules. By anintegration of equilibrium and evolution analysis methods, this paper reveals themechanisms of traffic flow evolution as well as the processes and conditions oftraffic network equilibrium, and enriches and develops traditional traffic assignmenttheories.
Finally, a sequential travel decision learning model is formulated based onCumulative Prospect Theory and the Bayes Law. After a deep analysis of thecharacters of sequential travel decisions as well as the connotations and affectingfactors of reference point, a route choice experiment is designed to investigate theupdating rules of reference point. The introduction of experimental research method not only provides notion and reference for empirical study of travel behavior, butalso creates conditions for Prospect Theory’s application in practice.
By an integration of normative research and empirical analysis, this paperapplies behavioral science to travel behavior analysis and modeling based on rationalbehavior assumptions and research method. The suggested models, algorithms andconclusions can provide theoretical foundation for further research of traffic issues,such as traffic assignment, dynamic route guidance, congestion pricing and regionaltraffic restriction, etc.
引文
[1]隽志才,宗芳,富晓艳. TDM政策实施及评价综述[J].中国软科学,2007,1:156-160.
[2] von Newmann J, Morgenstern O. Theory of games and economic behavior [M]. PrincetonUniversity Press,1944.
[3] Allais M, Hagen O E. Expected Utility Hypothesis and the Allias Paradox [M]. DordrecheHolland: D. Reidel Publishing Co.,1979.
[4] Ellsberg D. Risk, Ambiguity and the savage axioms [J]. Quarterly Journal of Economics,1961,75(4):643-669.
[5] Roth A E, Prasnikar V, Okuno-Fujiwara M, et al. Bargaining and market behavior in Jerusalem,Ljubljana, Pittsburgh, and Tokyo: an experimental study [J]. Bargaining and market behavior,1991,81(5):1068-1095.
[6] Simon H A. Behavioral model of rational choice [J]. Quarterly Journal of Economics,1955,69:99-120.
[7] Kahneman D, Tversky A. Prospect theory: an analysis of decision under risk [J]. Econometrica,1979,47(2):263-292.
[8] Tversky A, Kahneman D. Advances in prospect theory: Cumulative representation ofuncertainty [J]. Risk Uncertainty,1992,5:297-323.
[9] Fujii S, Kitamura R. Drivers’ mental representation of travel time and departure time choice inuncertain traffic network conditions [J]. Networks and Spatial Economics,2004,4(3):243-256.
[10] Jou R C, Kitamura R, Weng M C, et al. Dynamic commuter departure time choice underuncertainty [J]. Transportation Research Part A,2008,42(5):774-783.
[11] Konstantinos V K, Yawa D A, Donald L F, et al. Risk attitude reversals in drivers' routechoice when range of travel time information is provided [J]. Human Factors: The Journal of theHuman Factors and Ergonomics Society,2002,44(3):466-473.
[12] Wardrop J G. Some theoretical aspects of road traffic research [J]. Proceedings of the Instituteof Civil Engineers,1952,1(2):325-378.
[13] Patriksson M. The Traffic Assignment Problem-Model and Method [M]. The Netherlands:VSP,1994.
[14] Avineri E, Prashker J N. Violations of expected utility theory in route-choice statedpreferences: the certainty effect and inflating of small probabilities [J]. Transportation ResearchRecord,2004,(1894):222-229.
[15] de Palma A, Picard N. Route choice decision under travel time uncertainty [J]. TransportationResearch Part A,2005,39(4):295-324.
[16] Avineri E. A cumulative prospect theory approach to passengers’ behavior modeling: waitingtime paradox revisited [J]. Journal of Intelligent Transportation Systems,2004,8(4):195-204.
[17] Stathopoulos A, Dimitriou L. Fuzzy modeling approach for combined forecasting of urbantraffic flow [J]. Computer-Aided Civil and Infrastructure Engineering,2008,23:521-535.
[18] Erev I, Bereby-Meyer Y, Roth A. The effect of adding a constant to all payoffs: experimentalinvestigation and implications for reinforcement learning models [J]. Journal of EconomicBehavior and Organization,1999,39:111-128.
[19] Horowitz J L. The stability of stochastic equilibrium in a two-link transportation network [J].Transportation Research B,1984,18:13-28.
[20] Nakayama S. Bayesian learning, day-to-day adjustment process, and stability of WardropEquilibrium [J]. Transportation and Traffic Theory,2009,21:425-440.
[21] Yang F. An evolutionary game theory approach to the day-to-day traffic dynamics [D].Madison: University of Wisconsin-Madison,2005.
[22]李振龙.诱导条件下驾驶员路径选择行为的演化博弈分析[J].交通运输系统工程与信息,2003,3(2):23-27.
[23]吴兵,李林波.交通拥挤的进化动态分析[J].中国公路学报,2006,19(3):106-110.
[24]关宏志,浦亮.基于演化博弈理论的有限理性交通选择行为模型[J].北京工业大学学报,2010,36(8):1077-1083.
[25]刘建美.诱导条件下的路径选择行为及协调方法研究[D].天津:天津大学,2010.
[26] Ben-Akiva M, Lerman S. Discrete choice analysis: Theory and application to travel demand[M].2000, Massachusetts: MIT Press,2000.
[27] Lee M S, McNally M G. An empirical investigation on the dynamic processes of activityscheduling and trip chaining [J]. Transportation,2006,33(6):553-565.
[28] Avineri E, Prashker J N. The impact of travel time information on travelers’ learning underuncertainty [J]. Transportation,2006,33(4):393-408.
[29] Ben-Elia E, Erev I, Shiftan Y. The combined effect of information and experience on drivers’route-choice behavior [J]. Transportation,2008,35(1):165-177.
[30] Adler J L. Investigating the learning effects of route guidance and traffic advisories on routechoice behavior [J]. Transportation Research Part C,2001,9(1):1-14.
[31] Selten R, Pitz T, Kube S, et al. Commuters route choice behavior[J]. Games and EconomicBehavior,2007,58:394-406.
[32] Jha M, Madanat M, Peeta S. Perception updating and day-to-day travel choice dynamics intraffic networks with information provision [J]. Transportation Research Part C,1998,6(3):189-212.
[33] Ettema D, Tamminga G, Timmermans H, et al. A micro-simulation model system of departuretime using a perception updating model under travel time uncertainty [J]. Transportation ResearchPart A,2005,39(1):325-344.
[34]刘天亮,黄海军,陈剑.考虑风险规避和认知更新的日常择路行为演进[J].交通运输工程学报,2008,8(4):90-94.
[35]范文博,李志纯,蒋葛夫.基于参考依赖法的出行者日常路径选择行为建模[J].交通运输工程学报,2009,9(1):96-99.
[36]陆化普,殷亚峰.交通网络均衡分析的变分不等式方法[J].公路交通科技,1997,6:24-29.
[37] Daganzo C F, Sheffi Y. On stochastic models of traffic assignment [J]. Transportation Science,1977(11):253-274.
[38] Nagurney A. A multiclass, multicriteria traffic network equilibrium model [J]. Mathematicaland Computer Modeling,2000,32:393-411.
[39] Bekhor S, Ben-Akiva M E, Ramming M S. Estimating route choice models for large urbannetworks [C]. the9th World Conference on Transport Research.2001. Seoul, Korea.
[40] Chen A, Recker W W. Considering risk taking behavior in travel time reliability [R].2000,Institute of Transportation Studies (ITS), University of California, Irvine, USA.
[41] Lo H K, Tung Y K. Network with degradable links: capacity analysis and design [J].Transportation Research Part B,2003,37(4):345-363.
[42] Lo H K, Luo X W, Siu B W Y. Degradable transport network: travel time budget of travelerswith heterogeneous risk aversion [J]. Transportation Research Part B,2006,40(9):792-806.
[43] Lam W H K, Shao H, Sumalee A. Modeling impacts of adverse weather conditions on a roadnetwork with uncertainties in demand and supply [J]. Transportation Research Part B,2008,42(10):890-910.
[44] Siu B W Y, Lo H K. Travel time budget in doubly uncertain transport network: degradablecapacity and stochastic demand [J]. European Journal of Operational Research,2008,191(1):166-181.
[45] Chen A, Zhou Z. The α-reliable mean-excess traffic equilibrium model with stochastic traveltimes [J]. Transportation Research Part B,2010,44(4):493-513.
[46] Heydecker B G, Addison J D. Analysis of dynamic traffic equilibrium with departure timechoice [J]. Transportation Science,2005,39(1):39-57.
[47] Vickrey W S. Congestion theory and transport investment [J]. American Economic Review,1969,34:414-431.
[48] Hendrickson C, Kocur G. Schedule delay and departure time decisions in a deterministicmodel [J]. Transportation Science,1981,15:62-77.
[49] Arnott R, de Palma A, Lindsey R. Departure time and route choice for the morning trafficcommute [J]. Transportation Research,1990,24(3):209-228.
[50] Chen H K, Chang M S, Wang C Y. Dynamic capacitated user-optimal departure time/routechoice problem with time-window [J]. European Journal of Operational Research,2001,132:603-618.
[51] Small K. The scheduling of consumer activities: work trips [J]. American Economics Review,1982,72:467-479.
[52] Ran B, Hall R, Boyce D. A link-based variational inequality model for dynamic departuretime/route choice [J]. Transportation Research Part B,1996,30(1):31-46.
[53] Huang H J, Lam W H K. Modeling and solving the dynamic user equilibrium route anddeparture time choice problem in network with queues [J]. Transportation Research Part B,2002,36(3):253-273.
[54] Lam W H K, Li Z C, Huang H J, et al. Modelling time-dependent travel choice problems inroad networks with multiple user classes and multiple parking facilities [J]. TransportationResearch Part B,2006,40(5):368-395.
[55]任华玲,高自友.考虑出发时间选择的动态用户最优模型[J].交通运输系统工程与信息,2007,7(3):83-89.
[56]陈星光,周晶,李卓君等.多维动态用户最优出行选择的变分不等式模型[J].管理工程学报,2009,23(1):23-28.
[57] Zhang X N, Zhang H M. Simultaneous departure time/route choices in queuing networks anda novel paradox [J]. Networks&Spatial Economics,2010,10(1):93-112.
[58] Lim Y, Heydecker B G. Dynamic departure time and stochastic user equilibrium assignment[J]. Transportation Research Part B,2005,39:97-118.
[59] Watling D. Stability of the stochastic equilibrium assignment problem: a dynamical systemsapproach [J]. Transportation Research B,1999,33(4):281-312.
[60] Smith M. The stability of a dynamic model of traffic assignment-an application of a methodof Lyapunov [J]. Transportation Science,1984,18:245-252.
[61] Friesz T L, Bernstein D, Mehta N J, et al. Day-to-day dynamic network disequilibria andidealized traveler information systems[J]. Operations Research,1994,42(6):1120-1136.
[62] Zhang D, Nagurney A. On the local and global stability of a travel route choice adjustmentprocess [J]. Transportation Research Part B,1996,30(4):245-262.
[63] Nagurney A, Zhang D. Projected dynamical systems in the formulation, stability analysis, andcomputation of fixed-demand traffic network equilibrium [J]. Transportation Science,1997,31(2):147-158.
[64] Cascetta E. A stochastic process approach to the analysis of temporal dynamics intransportation networks [J]. Transportation Research B,1989,23(1):1-17.
[65] Hazelton M, Watling D. Computation of equilibrium distributions of Markov trafficassignment models [J]. Transportation Science,2004,38(3):331-342.
[66] Davis G, Nihan N. Large population approximations of a general stochastic traffic assignmentmodel [J]. Operations Research,1993,41(1):169-178.
[67] Hazelton M, Lee S, Polak J. Stationary states in stochastic process models of trafficassignment: a Markov Chain Monte Carlo approach [C]. the13th Symposium on Transportationand Traffic Theory.1996. Pergamon: Oxford.
[68]郭仁拥,黄海军. ATIS环境下交通配流的动态演化模型[J].管理科学学报,2008,11(2):12-19.
[69]徐红利.基于有限理性的城市交通系统均衡与拥挤收费策略研究[D].南京:南京大学,2011.
[70] Roth A, Erev I. Learning in extensive form games: experimental data and simple dynamicmodels in the intermediate term [J]. Games and Economic Behavior,1995,8(1):163-212.
[71] Berger U. Fictitious play in2×n games [J]. Journal of Economic Theory,2005,120(2):139-154.
[72] Camerer C F, Ho T H. EWA learning in normal-form games [J]. Econometrica,1999,67(4):827-873.
[73] Gintis H. Strong reciprocity and human sociality [J]. Journal of Theoretical Biology,2000,206(2):169-179.
[74] Beckmann M, McGuire C B, Winsten C B. Studies in the Economics of Transportation [M].New Haven: Yale University Press,1956.
[75] Haurie A, Marcottet P. On the relationship between Nash-Cournot and Wardrop Equilibria [J].Networks,1985,15:295-308.
[76] Hollander Y, Prashker J N. The applicability of non-cooperative game theory in transportanalysis [J]. Transportation,2006,33(5):483-496.
[77] Fudenberg D, Levine D K. Theory of Learning in Games [M]. Cambridge: MIT Press,1998.
[78] Sandholm W H. Evolutionary implementation and congestion pricing [J]. Review ofEconomic Studies,2002,69:667-689.
[79]赵晗萍,冯允成,蒋家东.进化博弈模型中有限理性个体学习机制设计框架[J].系统工程,2005,23(9):16-19.
[80] Brenner T. Agent Learning Representation: Advice on Modelling Economic Learning [C]//Tesfatsion L, Kenneth L J. Handbook of Computational Economics. Elsevier,2006.
[81]朱宪辰.人类行为的法则:学习行为实验经济学研究[M].浙江大学出版社,2009:1-13.
[82] Yanmaz-Tuzel O, Ozbay K. Modeling learning impacts on day-to-day travel choice [J].Transportation and Traffic Theory,2009,19:387-401.
[83] Arentze T A, Timmermans H J P. Information gain, novelty seeking and travel: a model ofdynamic activity-travel behavior under conditions of uncertainty [J]. Transportation Research PartA,2005,39(1):125-145.
[84]徐红利,周晶,徐薇.考虑参考点依赖的随机网络用户均衡与系统演化[J].系统工程理论与实践,2010,30(12):2283-2289.
[85] Prelec D. The probability weighting function [J]. Econometrica,1998,66(3):497-527.
[86] Senbil M, Kitamura R. Reference points in commuter departure time choice: a test ofalternative decision frames [J]. Journal of Intelligent Transport Systems,2004,8(1):19-31.
[87] Wu G, Gonzalez R. Curvature of the probability weighting function [J]. Management Science,1996,42(12):1676-1690.
[88] Rieger M, Wang M. Prospect theory for continuous distributions [J]. Journal of Risk andUncertainty,2008,36(1):83-102.
[89] Pratt J W. Risk aversion in the small and in the large [J]. Econometrica,1964,32:122-136.
[90] Arrow K J. The role of securities in the optimal allocation of risk bearing [J]. Review ofEconomic Studies,1964,31:91-96.
[91] Glimcher P, Fehr E, Camerer C, et al. Handbook of Neuro-economics [M]. San Diego, C A:Academic Press,2008.
[92] Camerer C F, Ho T H. Violations of the betweenness axiom and nonlinearity in probability [J].Journal of Risk and Uncertainty,1994,8(2):167-196.
[93] Bleichrodt H, Pinto J L. A parameter-free elicitation of the probability weighting function inmedical decision analysis [J]. Management Science,2000,46:1485-1496.
[94] Abdellaoui M. Parameter-free elicitation of utilities and probability weighting functions [J].Management Science,2000,46:1497-1512.
[95] Gurevich G, Kliger D, Levy O. Decision-making under uncertainty-A field study ofcumulative prospect theory [J]. Journal of Banking and Finance,2009,33(7):1221-1229.
[96] Schwanen, T. and Ettema, D. Coping with unreliable transportation when collecting children:examining parents’ behavior with cumulative prospect theory [J]. Transportation Research Part A,2009,43(5):511-525.
[97] Stott H P. Cumulative prospect theory’s functional menagerie [J]. Journal of Risk andUncertainty,2006,32(2):101-130.
[98] Van de Kaa E J. Assessment of the Value of Travel Time from Stated Choice Surveys: TheTreatment of Lexicographic Answering [C]. European Transport Conference.2006. Strasbourg,France.
[99] Van de Kaa E J. Prospect Theory and choice behaviour strategies: review and synthesis ofconcepts from social and transport sciences [J]. European Journal of Transport and InfrastructureResearch,2010,10(4):299-329.
[100] Avineri E, Bovy P H L. Parameter identification of Prospect Theory model for travel choiceanalysis [J]. Transportation Research Record,2008,2082:141-147.
[101] Novemsky D, Kahneman D. The boundaries of loss aversion [J]. Journal of MarketingResearch,2005,42(2):119-128.
[102] Senbil M, Kitamura R. Heterogeneity in commuter departure time decision: a prospecttheoretic approach [C]//Attoh-Okine N O, Ayyub B. Applied Research in Uncertainty Modelingand Analysis,2004:369-398.
[103] Schmidt U, Zank H. What is loss aversion?[J] Risk Uncertainty,2005,30:157-167.
[104] Herne K. Testing the reference-dependent model: an experiment on asymmetricallydominated Reference Points [J]. Journal of Behavioral Decision Making,1998,11:181-192.
[105] Hu W. Bargains or Rip-offs? Reference price effects in conjoint stated demand [J]. Journalof Agricultural and Resource Economics,2007,32(2):256-272.
[106] de Blaeij A T, van Vuuren D J. Risk perception of traffic participants [J]. Accident Analysisand Prevention,2003,35:167-175.
[107] de Borger B, Fosgerau M. The trade-off between money and travel time: a test of the theoryof reference-dependent preferences [J]. Journal of Urban Economics,2008,64:101-115.
[108] Frederick S. Loewenstein G H. Adaptation in Kahneman D, Diener E. and Schwarz N.well-being: the Foundations of Hedonic Psychology [M]. New York: Russell Sage Foundation,1999.
[109] Camerer C F. Prospect Theory in the wild: evidence from the field in Kahneman D. andTversky A. Choices, Values and Frames [R]. New York: Russell Sage Foundation,2000.
[110] Bleichrodt H, Pinto J L, Wakker P P. Making descriptive use of Prospect Theory to improvethe prescriptive use of Expected Utility [J]. Management Science,2001,47(11):1498-1514.
[111] Wang M, Fischbeck P S. Incorporating framing into Prospect Theory modeling: amixture-model approach [J]. The Journal of Risk and Uncertainty,2004,29(2):181-197.
[112] Slovic P, Finucane M L, Peters E, et al. Risk as analysis and risk as feelings: some thoughtsabout affect, reason, risk, and rationality [J]. Risk Analysis,2004,24(2):311-322.
[113] Yates F J, Stone E R. The risk construct: Risk-taking behavior [M]. New York: Wiley,1992.
[114] Van de Kaa E J. Extended Prospect Theory: Findings on Choice Behaviour from Economicsand Behavioural Sciences and their Relevance for Travel Behaviour [M]. Delft: TRAIL,1998.
[115] Mazumdar T, Raj S P, Sinha I. Reference price research: review and propositions [J]. Joumalof Marketing,2005,69(10):84-102.
[116] Avineri E, Prashker J N. Sensitivity to uncertainty: the need for a paradigm shift [J].Transportation Research Record,2003,1854:90-98.
[117] Knetsch J L. Biased valuations, damage assessments, and policy choices: the choice ofmeasure matters [J]. Ecological Economics,2007,63(4):684-689.
[118] Xu H L, Lou Y Y, Yin Y F, et al. A prospect-based user equilibrium model with endogenousreference points and its application in congestion pricing [J]. Transportation Research Part B,2011,45(2):311-328.
[119] Boles T L, Messick D M. A reverse outcome bias: the influence of Multiple ReferencePoints on the Evaluation of Outcomes and Decisions [J]. Organizational Behavior and HumanDecision Processes,1995,6(3):262-275.
[120] Zhu W, Timmermans H J P. Decision making model incorporating choice of decision criteria[C]. the89th TRB Annual Meeting.2010. Washington, D.C.
[121] Gao S, Frejinger E, Ben-Akiva M. Adaptive route choices in risky traffic networks: aprospect theory approach [J]. Transportation Research Part C,2010,18(5):727-740.
[122] Schul Y, Mayo R. Searching for certainty in an uncertain world: the difficulty of giving upthe experiential for the rational mode of thinking [J]. Journal of Behavioral Decision Making,2003,16:93-106.
[123] Avineri E. Incorporating fuzzy Reference Points into applications of travel choice modeling[C]//Avineri E, K ppen M, Sunitiyoso Y, etl. Applications of Soft Computing: Updating the Stateof Art. Germany: Springer-Verlag,2009.
[124] Avineri E. The effect of reference point on stochastic network equilibrium [J].Transportation Science,2006,40(4):409-420.
[125] Kristensen H, Garling T. Adoption of cognitive reference points in negotiations [J]. ActaPsychologica,1997:277-288.
[126] de Palma A, Ben-Akiva M, Brownstone D, et al. Risk, uncertainty and discrete choicemodels [J]. Marketing Letters,2008,19:269-285.
[127]张杨,贾建民,黄庆.城市交通中车辆择路行为实证研究[J].管理科学学报,2007,22(5):78-85.
[128] White S B, Valley K L, Bazerman M H, et al. Alternative models of price behavior in dyadicnegotiations: Market prices, reservation prices, and negotiator assumptions [J]. OrganizationalBehavior and Human Decision Processes,1994,57(3):430-447.
[129] Munro A, Sugden R. On the theory of reference-dependent preference [J]. Journal ofEconomic Behavior&Organization,2003,50(4),407-428.
[130] Cao S H, Yuan Z Z, Li Y H, et al. Model for road network stochastic user equilibrium basedon bi-level programming under the action of the traffic flow guidance system [J]. Journal ofTransportation Systems Engineering and Information Technology,2007,7(4):36-42.
[131] Connors R D, Sumalee A. A network equilibrium model with travelers' perception ofstochastic travel times [J]. Transportation Research Part B,2009(43):614-624.
[132] Michea A, Polak J. Modelling risky choice behaviour: evaluating alternatives to expectedutility theory [C]. the11th International Conference on Travel Behaviour Research.2006. Kyoto,Japan.
[133] Timmermans H. On the (ir)relevance of Prospect Theory in modelling uncertainty in traveldecisions [J]. European Journal of Transport and Infrastructure Research,2010,10(4):368-384.
[134] Van Wee B. Prospect Theory and travel behaviour: a personal reflection based on a seminar[J]. European Journal of Transport and Infrastructure Research,2010,10(4):385-394.
[135] Knight F H. Risk, Uncertainty and Profit [M]. Boston: Houghton Mif-flin,1921.
[136]徐元栋,黄登仕,刘思峰.奈特不确定性下的行为决策理论研究综述[J].系统管理学报,2008,17(5):481-489.
[137]赵勇,王清,陈阳.基于有限感知的决策理性模型[J].系统工程理论与实践,2010,30(2):339-346.
[138]张秀丽.基于个体行为的资产定价模型研究[M].北京:经济科学出版社,2009.
[139] Loomes G, Sugden R. Regret Theory: an alternative theory of rational choice underuncertainty [J]. The Economic Journal,1982,92:805-824.
[140] Ajzen I, Fishbein M. Understanding Attitudes and Predicting Social Behaviour [M]. PrenticeHall, New York,1982.
[141] Quiggin J. A theory of anticipated utility [J]. Journal of Economic Behavior andOrganization,1982,3(4):497-527.
[142] Bonsall P. Traveller behavior: decision-making in an unpredictable world [J]. IntelligentTransportation Systems,2004,8:45-60.
[143] Van Lint J W C, van Zuylen H J, Tu H. Travel time unreliability on freeways: why measuresbased on variance tell only half the story [J]. Transport Research Part A,2008,42(1):258-277.
[144] Shao H, Lam W H K, Tam M L. A reliability-based stochastic traffic assignment model fornetwork with multiple user classes under uncertainty in demand [J]. Networks and SpatialEconomics,2006,63(4):173-204.
[145] Siu B W Y, Lo H K. Doubly uncertain transportation network: degradable capacity andstochastic demand [J]. European Journal of Operational Research,2008,191(1):166-181.
[146] Di S. Traffic Equilibrium and System Reliability In Stochastic Transportation Network [D].University of Wilsconsin-Madison,2007.
[147] Tatineni M, Boyce D E, Mirchandani P. Comparisons of deterministic and stochasticnetwork traffic loading models [J]. Transportation Research Record,1997,1607:16-23.
[148] Ben-Elia E, Shiftan Y. Which road do I take? A learning-based model of route-choicebehavior with real-time information [J]. Transportation Research Part A,2010,44(1):249-264.
[149]黄海军.交通行为建模-问题与机会[J].交通运输系统工程与信息,2002,2(1):24-29.
[150] Avineri E, Prashker J N. Sensitivity to travel time variability: Travelers learning perspective[J]. Transportation Research Part C,2005,13(2):157-183.
[151] Han Q, Dellaert B, van Raaij F, et al. Integrating Prospect Theory and Stackelberg Games toModel Strategic Dyad Behavior of Information Providers and Travelers: Theory and NumericalSimulations [J]. Transportation Research Record,2005,1926:181-188.
[152] Becker G S. Crime and punishment: An economic approach [J]. Political Economics,1968,76:169-217.
[153] Benartzi S, Thaler R. Myopic loss aversion and the equity premium puzzle [J]. QuarterlyJournal of Economics,1995,110:75-92.
[154] Gneezy U, Potters J. An experiment on risk taking and evaluation periods [J]. QuarterlyJournal of Economics,1997,112:631-645.
[155] Barron G, Erev I. Small feedback-based decisions and their limited correspondence todescription based decisions [J]. Journal of Behavioral Decision Making,2003,16:215-233.
[156] March J G. Learning to be risk averse [J]. Psychology Review,1996,103:309-319.
[157] Schmidt U, Zank H. Risk aversion in cumulative prospect theory [J]. Management Science,2008,54(1):208-216.
[158] Camerer C. Individual decision making [A]//Handbook of Experimental Economics.Princeton N J: Princeton University Press,1995.
[159] Ross D.经济学理论与认知科学:微观解释[M].贾拥民译.北京:中国人民大学出版社,2011.
[160] Yin Y Y, William H K, Lam H I. Reliability assessment on transit network service [C]. thefirst International Symposium on Transportation Network Reliability.2001. Kyoto, Japan.
[161] Chen A, Recker W. Considering risk-taking behavior in travel time reliability [C]. the80thTransportation Research Board Annual Meeting.2000. Washington D.C.
[162] Chen A, Ji Z, Recker W. Travel time reliability with risk-sensitive travelers [J].Transportation Research Record,2002,1783:27-33.
[163] Henry L X, Recker W, Chen A. Uncovering the contribution of travel time reliability todynamic route choice using real-time loop data [J]. Transportation Research A,2004,38(6):435-453.
[164] Bell M G H, Iida Y. Transportation Network Analysis [M]. John Wiley&Son Inc,1997.
[165] Ulrich S. Reference dependence in cumulative prospect theory [J]. Journal of MathematicalPsychology,2003,47(2):122-131.
[166] Sheffi Y. Urban transportation networks: equilibrium analysis with mathematicalprogramming methods [M]. Englewood Cliffs: Prentice-Hall,1985.
[167]周晶.随机交通均衡配流模型及其等价的变分不等式问题[J].系统科学与数学,2003,23(1):120-127.
[168] Nguyen S, Dupius C. An efficient method for computing traffic equilibria in networks withasymmetric transportation costs [J]. Transport Science,1984,18(2):185-202.
[169] Szeto W Y, Lo H K. The impact of advanced traveler information services on travel time andschedule delay costs [J]. Journal of Intelligent Transportation Systems,2005,9(1):47-55.
[170] Yang H. Multiple equilibrium behaviors and advanced traveler information systems withendogenous market penetration [J]. Transportation Research B,1998,32(3):205-218.
[171] Iida Y, Akiyama T, Uchida T. Experimental analysis of dynamic route choice behavior [J].Transport Research, Part B,1992,26(1):17-32.
[172] Friedman D. On economic applications of Evolutionary Game Theory [J]. Journal ofEvolutionary Economics,1998,8(1):15-43.
[173] Yang F, Zhang D. Day-to-day stationary link flow pattern [J]. Transportation Research PartB: Methodological,2009,43(1):119-126.
[174] Hofbauer J, Sandholm W H. Stable games and their dynamics [J]. Journal of EconomicTheory,2009,144(4):1665-1693.
[175] Taylor P D, Jonker L B. Evolutionarily Stable Strategy and Game Dynamics [J]. MathBioscience,1978,40:145-156.
[176] Gilboa I, Matsui A. Social stability and equilibrium [J]. Econometrica,1991,59:859-867.
[177] Brown G, von Neumann J. Solutions of games by differential equations[C]//Kuhn H W,Tucker A W. Contributtions to the theory of games. Princeton: Princeton University,1950.
[178] Nash J. Non-cooperative games [J]. Annals of Mathematics,1951,54:286-295.
[179] Weibull J. Evolutionary Game Theory [M]. Cambridge: MIT Press,1995.
[180] Hahn W. Theory and application of Lyapunov’s Derect Method [M]. New Jersey:Pretice-Hall,1963.
[181] Friedman, M. The Methodology of Positive Economics [M]. Chicago: University ofChicago Press,1953.
[182] Celen B, Kariv S. An experimental test of observational learning under imperfectinformation [J]. Economic Theory,2005,26(3):677-699.
[183]朱宪辰,李妍绮,曾华翔.不完美信息下序贯决策行为的一项实验考察:关于羊群行为的贝叶斯模型实验检验[J].经济研究,2008,8(6):145-156.
[184] Berger J O. Statistical Decision Theory and Bayesian Analysis [M]. New York:Springer-Verlag,1985.
[185] McFadden D. Disaggregate Behavioral Travel Demand’s RUM Side: a30YearTetrospective in D. Hensher’s Travel Behaviour Research: the Leading Edge [M]. Oxford:Pergamon Press,2000.
[186] Ben-Akiva M, McFadden D, Train K, et al. Hybrid choice models: progress and challenges[M]. Marketing Letters,2002,13:163-175.
[187] Fong C P S, Wyer R S. Culture, social, and emotional determinants of decisions underuncertainty [J]. Organizational Behavior and Human Decision Processes,2003,90(3):304-322.
[188] Loewenstein G F, Weber E U, Hsee C K, et al. Risk as feelings [J]. Psychological Bulletin,2001,127(3):267-286.
[189] Mellers B A, Schwartz A, Ritov I. Emotion based choice [J]. Journal of ExperimentalPsychology: General,1999,128(9):332-345.
[190] Razo M, Gao S. Strategic thinking and risk attitudes in route choice: Stated preferenceapproach [J]. Transportation Research Record,2010,2156:28-35.
[191] Bogers E A I. Viti F, Hoogendoorn S P. Joint modeling of ATIS, habit and learning impactson route choice by laboratory simulator experiment [C]. the84th annual meeting of theTransportation Research Board.2005. Washington D. C.
[192] Booij A S, van Praag B M S, van de Kuilen G. A parametric analysis of prospect theory’sfunctional for the general population [J]. Theory and Decision,2010,68:115-148.
[193] Krafft M. An empirical investigation of the antecedents of sales force control system [J].Journal of Marketing,1999,63(7):120-134.
[194] Ross W T. Performance against quota and the call selection decision [J]. Journal ofMarketing Research,1991,28(8):292-306.