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Dynamic Decision Behavior and Optimal Guidance Through Information Services: Models and Experiments

  • Dirk Helbing
Conference paper

Abstract

In this contribution, dynamical models for decision making with and without temporal constraints are developed and applied to opinion formation, migration, game theory, the self-organization of behavioral conventions, etc. These models take into account the non-transitive and probabilistic aspects of decisions, i.e. they reflect the observation that individuals do not always take the decision with the highest utility or payoff. We will also discuss issues like the freedom of decision making, the red-bus-blue-bus problem, and effects of pair interactions such as the transition from individual to mass behavior.

In the second part, the theory is compared with recent results of experimental games relevant to the route choice behavior of drivers. The adaptivity (“group intelligence”) with respect to changing environmental conditions and unreliable information is very astonishing. Nevertheless, we find an intermittent dynamical reaction to aggregate information similar to volatility clustering in stock market data, which leads to considerable losses in the average payoffs. It turns out that the decision behavior is not just driven by the potential gains in payoffs. To understand these findings, one has to consider reinforcement learning, which can also explain the empirically observed emergence of individual response patterns. Our results are highly significant for predicting decision behavior and reaching the optimal distribution of behaviors by means of decision support systems. These results are practically relevant for any information service provider.

Keywords

Test Person Route Choice User Equilibrium Decision Behavior Transportation Research Record 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    D. Helbing, Traffic and related self-driven many-particle systems, Reviews of Modern Physics 73, 1067–1141 (2001).CrossRefGoogle Scholar
  2. 2.
    J. H. Hagel and A. E. Roth (Eds.), The Handbook of Experimental Economics (Princeton University, Princeton, NJ, 1995).Google Scholar
  3. 3.
    A. Shleifer, Inefficient Markets: An Introduction to Behavioral Finance (Clarendon Lectures, Oxford University, Oxford, 2000).Google Scholar
  4. 4.
    W. B. Arthur, Inductive reasoning and bounded rationality, American Econonmic Review 84, 406–411 (1994).Google Scholar
  5. 5.
    D. Challet and Y.-C. Zhang, Emergence of cooperation and organization in an evolutionary game, Physica A 246, 407ff (1997).Google Scholar
  6. 6.
    D. Challet and Y.-C. Zhang, On the minority game: Analytical and numerical studies, Physica A 256, 514–532 (1998).CrossRefGoogle Scholar
  7. 7.
    D. Challet, M. Marsili, and Y.-C. Zhang, Modeling market mechanism with minority game Physica A 276, 284–315 (2000).MathSciNetGoogle Scholar
  8. 8.
    H. C. Rachlin, Behavior and Learning (Freeman, San Francisco, 1976).Google Scholar
  9. 9.
    H. C. Rachlin and W. M. Baum, Effects of alternative reinforcement: Does the source matter?, Journal of the Experimental Analysis of Behavior 18, 231–241 (1972).CrossRefGoogle Scholar
  10. 10.
    S. R. Schroeder and J. G. Holland, Reinforcement of eye movement with concurrent schedules, Journal of the Experimental Analysis of Behavior 12, 897–903 (1969).CrossRefGoogle Scholar
  11. 11.
    G. T. Fechner, Elemente der Psychophysik (1860).Google Scholar
  12. 12.
    T. A. Domencich and D. M. McFadden, Urban Travel Demand. A Behavioral Analysis, pp. 61–69, (North-Holland, Amsterdam, 1975).Google Scholar
  13. 13.
    J. de D. Ortúzar and L. G. Willumsen, Modelling Transport, Chap. 7: Discrete-Choice Models (Wiley, Chichester, 1990).Google Scholar
  14. 14.
    M. Ben-Akiva, D. M. McFadden et al., Extended framework for modeling choice behavior, Marketing Letters 10, 187–203 (1999).CrossRefGoogle Scholar
  15. 15.
    F. Reif, Fundamentals of Statistical and Thermal Physics, pp. 202ff, 229ff (McGraw-Hill, Singapore, 1965).Google Scholar
  16. 16.
    W. G. V. Rosser, An Introduction to Statistical Physics, pp. 108f. (Horwood, Chichester, 1982).Google Scholar
  17. 17.
    H. Haken, Information and Self-Organization (Springer, Berlin, 1988).MATHGoogle Scholar
  18. 18.
    D. Helbing, Stochastische Methoden, nichtlineare Dynamik und quantitative Modelle sozialer Prozesse (Shaker, Aachen, 1996).Google Scholar
  19. 19.
    D. Helbing, Quantitative Sociodynamics (and references therein) (Kluwer Academic, Dordrecht, 1995).Google Scholar
  20. 20.
    F. Heider, Attitudes and cognitive organization, Journal of Psychology 21, 107–112 (1946).CrossRefGoogle Scholar
  21. 21.
    F. Heider, The Psychology of Interpersonal Relations (Wiley, New York, 1958).Google Scholar
  22. 22.
    D. Cartwright and F. Harary, Structural balance: A generalization of Heider’s theory, Psychological Review 63, 277–293 (1956).CrossRefGoogle Scholar
  23. 23.
    C. E. Osgood and P. H. Tannenbaum, The principle of congruity in the prediction of attitude change, Psychological Review 62, 42–55 (1955).CrossRefGoogle Scholar
  24. 24.
    L. Festinger, A Theory of Cognitive Dissonance (Row & Peterson, Evanston, IL, 1957).Google Scholar
  25. 25.
    S. S. Brehm, The Application of Social Psychology to Clinical Practice (Wiley, New York, 1976).Google Scholar
  26. 26.
    J. Binder, G. Haag, and M. Koller, Modelling and simulation of migration, regional employment development and regional gross wage payment in Germany: The bottom-up approach, in Regional Economies in Transition (Research Report 02:1, University of Trollhättan/Uddevalla, 2002).Google Scholar
  27. 27.
    H. Feger (Ed.), Studien zur intraindividuellen Konfliktforschung (Huber, Bern, 1977).Google Scholar
  28. 28.
    H. Feger, Konflikterleben und Konfliktverhalten (Huber, Bern, 1978).Google Scholar
  29. 29.
    A. Babloyantz and A. Destexhe, Strange attractors in the human cortex, in Temporal Disorder in Human Oscillatory Systems, L. Rensing, U. van der Heiden, and M. C. Mackey (Eds.) (Springer, Heidelberg, 1987).Google Scholar
  30. 30.
    A. Babloyantz, C. Nicolis, and M. Salazar, Evidence of chaotic dynamics of brain activity during the sleep cycle, Physics Letters A 111, 152 (1985).CrossRefGoogle Scholar
  31. 31.
    C. E. Osgood, G. J. Suci, and P. H. Tannenbaum, The Measurement of Meaning (University of Illinois Press, Urbana, 1957).Google Scholar
  32. 32.
    P. H. Douglas, The Theory of Wages, pp. 132–135 (Macmillan, New York, 1934).Google Scholar
  33. 33.
    W. Nicholson, Microeconomic Theory, pp. 90ff, 111ff (Dryden Press, Fort Worth, 5th edition, 1992).Google Scholar
  34. 34.
    M. Ben-Akiva, J. Bottom, and M. S. Ramming, Route guidance and information systems, Int. J. Syst. Contr. Engin. 215, 317–324 (2001).Google Scholar
  35. 35.
    B. Libet, C. A. Gleason, E. W. Wright, and D. K. Pearl, Time of conscious intention to act in relation to onset of cerebral activity (readiness-potential), Brain 106, 623–642 (1983).CrossRefGoogle Scholar
  36. 36.
    P. Haggard and M. Eimer, On the relation between brain potentials and the awareness of voluntary movements, Experimental Brain Research 126, 128–133 (1999).CrossRefGoogle Scholar
  37. 37.
    J. H. Harvey, Attribution of freedom, in New Directions in Attribution Research, Chap. 4, J. H. Harvey, W. J. Ickes, and R. F. Kidd (Eds.) (Wiley, New York, 1976).Google Scholar
  38. 38.
    I. D. Steiner, Perceived freedom, in Advances in Experimental Social Psychology, L. Berkowitz (Ed.) (Academic Press, New York, 1970).Google Scholar
  39. 39.
    J. W. Brehm, Responses to Loss of Freedom: A Theory of Psychological Reactance, (General Learning Press, Morristown, NJ, 1972).Google Scholar
  40. 40.
    J. W. Brehm, A Theory of Psychological Reactance (Academic Press, New York, 1966).Google Scholar
  41. 41.
    C. B. Wortman and J. W. Brehm, Responses to uncontrollable outcomes: An integration of reactance theory and the learned helplessness modell, in Advances in Experimental Social Psychology, pp. 277–336, L. Berkowitz (Ed.) (Academic Press, New York, 1975).Google Scholar
  42. 42.
    W. Weidlich and G. Haag, Concepts and Models of a Quantitative Sociology. The Dynamics of Interacting Populations (Springer, Berlin, 1983).MATHGoogle Scholar
  43. 43.
    W. Weidlich, Physics and social science-The approach of synergetics, Physics Reports 204, 1–163 (1991).MathSciNetCrossRefGoogle Scholar
  44. 44.
    W. Weidlich, Sociodynamics. A Systematic Approach to Mathematical Modelling in the Social Sciences, (Harwood Academic, Amsterdam, 2000).MATHGoogle Scholar
  45. 45.
    D. Helbing, Microscopic foundation of stochastic game dynamical equations, in Game Theory, Experience, Rationality, pp. 211–224, W. Leinfellner and E. Köhler (Eds.) (Kluwer Academic, Dordrecht, 1998).Google Scholar
  46. 46.
    D. Helbing, A mathematical model for behavioral changes by pair interactions and its relation to game theory, Angewandte Sozialforschung 18(3), 117–132 (1994).Google Scholar
  47. 47.
    D. Helbing, Stochastic and Boltzmann-like models for behavioral changes, and their relation to game theory, Physica A 193, 241–258 (1993).MathSciNetCrossRefGoogle Scholar
  48. 48.
    D. Helbing, Interrelations between stochastic equations for systems with pair interactions, Physica A 181, 29–52 (1992).MathSciNetCrossRefGoogle Scholar
  49. 49.
    D. Helbing, A mathematical model for the behavior of individuals in a social field, Journal of Mathematical Sociology 19(3), 189–219, (1994).CrossRefGoogle Scholar
  50. 50.
    R. S. Burt, Towards a Structural Theory of Action. Network Models of Social Structure, Perception, and Action, (Academic Press, New York, 1982).Google Scholar
  51. 51.
    N. Braun, Socially Embedded Exchange (Lang, Frankfurt/Main, 1993).Google Scholar
  52. 52.
    A. Krawiecki, J. A. Holyst, and D. Helbing, Volatility clustering and scaling for financial time series due to attractor bubbling, submitted.Google Scholar
  53. 53.
    D. Helbing, I. Farkas, and T. Vicsek, Simulating dynamical features of escape panic, Nature 407, 487–490 (2000).CrossRefGoogle Scholar
  54. 54.
    M. Fishbein and I. Ajzen, Belief, Attitude, Intention and Behavior: An Introduction to Theory and Research, (Addison-Wesley, Reading, MA, 1975).Google Scholar
  55. 55.
    N. H. Anderson, Group performance in an anagram task, Journal of Social Psychology 55, 67–75 (1961).CrossRefGoogle Scholar
  56. 56.
    H. H. Kelley and J. W. Thibaut, Group problem solving, in The Handbook of Social Psychology, Vol. 4, G. Lindzey and E. Aronson (Eds.) (Addison-Wesley, Reading, MA, 1969).Google Scholar
  57. 57.
    P. R. Laughlin, N. L. Kerr, J. H. Davis, H. M. Half, and K. A. Marciniak, Group size, member ability, and social decision schemes on an intellective task, Journal of Personality and Social Psychology 31, 522–535 (1975).CrossRefGoogle Scholar
  58. 58.
    R. Pearl, Studies in Human Biology (Williams & Wilkins, Baltimore, 1924).Google Scholar
  59. 59.
    P. F. Verhulst, Nouveaux Mémoires de l’Académie Royale des Sciences et des Belles-Lettres de Bruxelles 18, lff (1845).Google Scholar
  60. 60.
    D. J. Bartholomew, Stochastic Models for Social Processes (Wiley, London, 1967).Google Scholar
  61. 61.
    E. W. Montroll and W. W. Badger, Introduction to Quantitative Aspects of Social Phenomena (Gordon and Breach, New York, 1974).Google Scholar
  62. 62.
    R. L. Hamblin, R. B. Jacobsen, and J. L. L. Miller, A Mathematical Theory of Social Change (New York, 1973).Google Scholar
  63. 63.
    M. Olinick, An Introduction to Mathematical Models in the Social and Life Sciences, pp. 59–65, (Addison-Wesley, Reading, MA, 1978).Google Scholar
  64. 64.
    E. Ravenstein, The birthplaces of the people and the laws of migration, The Geographical Magazine III, 173–177, 201–206, 229–233 (1876).Google Scholar
  65. 65.
    G. K. Zipf, The PIP2/D hypothesis on the intercity movement of persons, American Sociological Review 11, 677–686 (1946).CrossRefGoogle Scholar
  66. 66.
    W. Weidlich and G. Haag (Eds.), Interregional Migration (Springer, Berlin, 1988).Google Scholar
  67. 67.
    G. Haag, Dynamic Decision Theory. Applications to Urban and Regional Topics (Kluwer Academics, Dordrecht, 1989).Google Scholar
  68. 68.
    D. Helbing, Boltzmann-like and Boltzmann-Fokker-Planck equations as a foundation of behavioral models, Physica A 196, 546–573 (1993).MathSciNetMATHCrossRefGoogle Scholar
  69. 69.
    K. Lewin, Field Theory in Social Science (Harper and Brothers, New York, 1951).Google Scholar
  70. 70.
    D. Helbing, A mathematical model for the behavior of pedestrians, Behavioral Science 36, 298–310 (1991).CrossRefGoogle Scholar
  71. 71.
    A. Nowak, J. Szamrej, and B. Latané, From private attitude to public opinion: A dynamic theory of social impact, Psychological Review 97, 362–376 (1990).CrossRefGoogle Scholar
  72. 72.
    M. Lewenstein, A. Nowak, and B. Latané, Statistical mechanics of social impact, Physical Review A 45, 763–776 (1992).MathSciNetCrossRefGoogle Scholar
  73. 73.
    R. Vallacher and A. Nowak (Eds.), Dynamic Systems in Social Psychology (Academic, New York, 1994).Google Scholar
  74. 74.
    K. Kacperski and J. A. Holyst, Phase transitions and hysteresis in a cellular automata-based model of opinion formation, Journal of Statistical Physics 84, 169–189 (1996).CrossRefGoogle Scholar
  75. 75.
    D. Helbing, Verkehrsdynamik. Neue physikalische Modellierungskonzepte (Springer, Berlin, 1997).MATHGoogle Scholar
  76. 76.
    D. Helbing and B. Tilch, Generalized force model of traffic dynamics., Physical Review E 58, 133–138 (1998).CrossRefGoogle Scholar
  77. 77.
    M. Treiber, A. Hennecke, and D. Helbing, Congested traffic states in empirical observations and microscopic simulations, Physical Review E 62, 1805–1824 (2000).CrossRefGoogle Scholar
  78. 78.
    D. Helbing and P. Molnar, Social force model for pedestrian dynamics, Physical Review E 51, 4282–4286 (1995).CrossRefGoogle Scholar
  79. 79.
    D. Helbing, I. Farkas, and T. Vicsek, Freezing by heating in a driven mesoscopic system, Physical Review Letters 84, 1240–1243 (2000).CrossRefGoogle Scholar
  80. 80.
    D. Helbing, Boltzmann-like and force models for behavioral changes, in Operations Research ‘83, pp. 251–254, A. Bachem, U. Derigs, M. Jünger, and R. Schrader (Eds.) (Physica, Heidelberg, 1994).Google Scholar
  81. 81.
    J. Hofbauer, P. Schuster, and K. Sigmund, A note on evolutionarily stable strategies and game dynamics, Journal of Theoretical Biology 81, 609–612 (1979).MathSciNetCrossRefGoogle Scholar
  82. 82.
    P. Taylor and L. Jonker, Evolutionarily stable strategies and game dynamics, Mathematical Biosciences 40, 145–156 (1978).MathSciNetMATHCrossRefGoogle Scholar
  83. 83.
    E. C. Zeeman, Population dynamics from game theory, in Global Theory of Dynamical Systems (1980).Google Scholar
  84. 84.
    J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems (Cambridge University Press, Cambridge, 1988).MATHGoogle Scholar
  85. 85.
    M. Eigen, The selforganization of matter and the evolution of biological macromolecules, Naturwissenschaften 58, 465 (1971).CrossRefGoogle Scholar
  86. 86.
    R. A. Fisher, The Genetical Theory of Natural Selection (Oxford University Press, Oxford, 1930).Google Scholar
  87. 87.
    D. Helbing, A mathematical model for behavioral changes by pair interactions, in Economic Evolution and Demographic Change. Formal Models in Social Sciences, pp. 330–348, G. Haag, U. Mueller, and K. G. Troitzsch (Eds.) (Springer, Berlin, 1992).Google Scholar
  88. K. H. Schlag, Why imitate, and if so, how? A bounded rational approach to multi-armed bandits, Discussion Paper No. B-361 (Department of Economics, University of Bonn).Google Scholar
  89. 89.
    A. J. Lotka, Analytical note on certain rhythmic relations in organic systems, Proceedings of the National Academy of Sciences of the United States of America 6, 410 (1920).CrossRefGoogle Scholar
  90. 90.
    A. J. Lotka, Elements of Mathematical Biology (Dover, New York, 1956).MATHGoogle Scholar
  91. 91.
    V. Volterra, Leçons sur la Théorie Mathématique de la Lutte pour la Vie (Gauthier-Villars, Paris, 1931).Google Scholar
  92. 92.
    N. S. Goel, S. C. Maitra, and E. W. Montroll, On the Volterra and other nonlinear models of interacting populations, Reviews of Modern Physics 43(2), 231–276 (1971).MathSciNetCrossRefGoogle Scholar
  93. 93.
    Th. G. Hallam, Community dynamics in a homogeneous environment, in Mathematical Ecology, T. G. Hallam and S. A. Levin (Eds.) (Springer, Berlin, 1986).Google Scholar
  94. 94.
    M. Peschel and W. Mende, The Predator-Prey Model (Springer, Wien, 1986).MATHGoogle Scholar
  95. 95.
    D. Helbing, A mathematical model for attitude formation by pair interactions, Behavioral Science 37, 190–214 (1992).CrossRefGoogle Scholar
  96. 96.
    D. Helbing, A stochastic behavioral model and a ‘microscopic’ foundation of evolutionary game theory, Theory and Decision 40, 149–179 (1996).MathSciNetMATHCrossRefGoogle Scholar
  97. 97.
    W. B. Arthur, Competing technologies, increasing returns, and lock-in by historical events, The Economic Journal 99, 116–131 (1989).CrossRefGoogle Scholar
  98. 98.
    M. Schreckenberg and R. Selten (Eds.), Human Behaviour and Traffic Networks (Springer, Berlin, 2002), to appear.Google Scholar
  99. 99.
    W. Barfield and T. Dingus, Human Factors in Intelligent Transportation Systems (Erlbaum, Mahwah, NJ, 1998).Google Scholar
  100. 100.
    J. Wahle, A. Bazzan, F. Klügl, and M. Schreckenberg, Decision dynamics in a traffic scenario, Physica A 287, 669–681 (2000).CrossRefGoogle Scholar
  101. 101.
    Articles in Route Guidance and Driver Information, IEE Conference Publications, Vol. 472 (IEE, London, 2000).Google Scholar
  102. 102.
    M. Ben-Akiva, A. de Palma, and I. Kaysi, Dynamic network models and driver information systems, Transportation Research A 25, 251–266 (1991).Google Scholar
  103. 103.
    H. S. Mahmassani and R. Jayakrishnan, System performance and user response under real-time information in a congested traffic corridor, Transportation Research A 25, 293–307 (1991).CrossRefGoogle Scholar
  104. 104.
    R. Arnott, A. de Palma, and R. Lindsey, Does providing information to drivers reduce traffic congestion?, Transportation Research A 25, 309–318 (1991).CrossRefGoogle Scholar
  105. 105.
    J. Adler, and V. Blue, Towards the design of intelligent traveler information systems, Transportation Research C 6, 157–172 (1998).CrossRefGoogle Scholar
  106. 106.
    H. S. Mahmassani and R. C. Jou, Transferring insights into commuter behavior dynamics from laboratory experiments to field surveys, Transportation Research A 34, 243–260 (2000).Google Scholar
  107. 107.
    P. Bonsall, P. Firmin, M. Anderson, I. Palmer, and P. Balmforth, Validating the results of a route choice simulator Transportation Research C 5, 371–387 (1997).Google Scholar
  108. 108.
    Y. Iida, T. Akiyama, and T. Uchida, Experimental analysis of dynamic route choice behavior, Transportation Research B 26, 17–32 (1992).CrossRefGoogle Scholar
  109. 109.
    P. S.-T. Chen, K. K. Srinivasan, and H. S. Mahmassani, Effect of information quality on compliance behavior of commuters under real-time traffic information, Transportation Research Record 1676, 53–60 (1999).CrossRefGoogle Scholar
  110. 110.
    R. D. Kühne, K. Langbein-Euchner, M. Hilliges, and N. Koch, Evaluation of compliance rates and travel time calculation for automatic alternative route guidance systems on freeways., Transportation Research Record 1554, 153–161 (1996).CrossRefGoogle Scholar
  111. 111.
    R. Hall, Route choice and advanced traveler information systems on a capacitated and dynamic network, Transportation Research C 4, 289–306 (1996).CrossRefGoogle Scholar
  112. 112.
    A. Khattak, A. Polydoropoulou, and M. Ben-Akiva, Modeling revealed and stated pretrip travel response to advanced traveler information systems, Transportation Research Record 1537, 46–54 (1996).CrossRefGoogle Scholar
  113. 113.
    M. Schreckenberg, R. Selten, T. Chamura, T. Pitz, and J. Wahle, Experiments on day-to-day route choice (and references therein), e-print www.trafficforum.org/01080701, submitted to Cooper@tive Tr@nsport@tion Dyn@miss (2001).
  114. 114.
    H. N. Koutsopoulos, A. Polydoropoulou, and M. Ben-Akiva, Travel simulators for data collection on driver behavior in the presence of information, Transportation Research C 3, 143–159 (1995).CrossRefGoogle Scholar
  115. 115.
    H. S. Mahmassani, and D.-G. Stephan, Experimental investigation of route and departure time choice dynamics of urban commuters. Transportation Research Records 1203, 69–84 (1988).Google Scholar
  116. 116.
    P. Bonsall, The influence of route guidance advice on route choice in urban networks, Transportation 19, 1–23 (1992).CrossRefGoogle Scholar
  117. 117.
    D. Helbing, M. Schönhof, and D. Kern, Volatile decision dynamics: Experiments, stochastic description, intermittency control, and traffic optimization, New Journal of Physics 4, 331–3316 (2002).CrossRefGoogle Scholar
  118. 118.
    D. Helbing, A section-based queueing-theoretical traffic model for congestion and travel time analysis, submitted to J. Phys. A: Math. Gen. (2003).Google Scholar
  119. 119.
    D. Fudenberg and D. Levine, The Theory of Learning in Games (MIT Press, Cambridge, MA, 1998).Google Scholar
  120. 120.
    M. W. Macy and A. Flache, Learning dynamics in social dilemmas, Proceedings of the National Academy of Sciences USA 99, Suppl. 3, 7229–7236 (2002).Google Scholar
  121. 121.
    R. N. Mantegna, and H. E. Stanley, Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge University, Cambridge, England, 1999).Google Scholar
  122. 122.
    S. Ghashghaie, W. Breymann, J. Peinke, P. Talkner, and Y. Dodge, Turbulent cascades in foreign exchange markets, Nature 381, 767–770 (1996).CrossRefGoogle Scholar
  123. 123.
    T. Lux and M. Marchesi, Scaling and criticality in a stochastic multi-agent model of a financial market, Nature 397, 498–500 (1999).CrossRefGoogle Scholar
  124. 124.
    J. Wahle, A. L. C. Bazzan, F. Klügl, and M. Schreckenberg, Anticipatory traffic forecast using multi-agent techniques, in Traffic and Granular Flow ’99, pp. 87–92, D. Helbing, H. J. Herrmann, M. Schreckenberg, and D. E. Wolf (Eds.) (Springer, Berlin, 2000).Google Scholar
  125. 125.
    M. Kraan, H. S. Mahmassani, and N. Huynh, Traveler Responses to Advanced Traveler Information Systems for Shopping Trips: Interactive Survey Approach, Transportation Research Record 1725, 116 (2000).CrossRefGoogle Scholar
  126. 126.
    K. K. Srinivasan and H. S. Mahmassani, Modeling Inertia and Compliance Mechanisms in Route Choice Behavior Under Real-Time Information, Transportation Research Record 1725, 45–53 (2000).CrossRefGoogle Scholar
  127. 127.
    M. Ben-Akiva and S. R. Lerman, Discrete Choice Analysis: Theory and Application to Travel Demand (MIT Press, Cambridge, MA, 1997).Google Scholar
  128. 128.
    S. Nakayama and R. Kitamura, Route Choice Model with Inductive Learning, Transportation Research Record 1725, 63–70 (2000).CrossRefGoogle Scholar
  129. 129.
    Y.-W. Cheung and D. Friedman, Individual learning in normal form games: Some laboratory results, Games and Economic Behavior 19(1), 46–76 (1997).MathSciNetMATHCrossRefGoogle Scholar
  130. 130.
    I. Erev and A. E. Roth, Predicting how people play games: Reinforcement learning in experimental games with unique, mixed strategy equilibria, American Economic Review 88(4), 848–881 (1998).Google Scholar
  131. 131.
    J. Nachabar, Prediction, optimization, and learning in repeated games, Econometrica 65, 275–309 (1997).MathSciNetCrossRefGoogle Scholar
  132. 132.
    J. B. van Huyck, R. C. Battlio, and R. O. Beil, Tacit coordination games, strategic uncertainty, and coordination failure, American Economic Review 80(1), 234–252 (1990).Google Scholar
  133. 133.
    J. B. van Huyck, J. P. Cook, and R. C. Battlio, Selection dynamics, asymptotic stability, and adaptive behavior, Journal of Political Economy 102(5), 975–1005 (1994).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Dirk Helbing
    • 1
    • 2
    • 3
  1. 1.Institute for Economics and Traffic, Faculty of Traffic Sciences “Friedrich List”Dresden University of TechnologyDresdenGermany
  2. 2.Collegium Budapest — Institute for Advanced StudyBudapestHungary
  3. 3.CCM—Centro de Ciências MatemáticasUniversidade da Madeira, Campus Universitário da PenteadaFunchal, MadeiraPortugal

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