Abstract
The Braess Paradox (BP) is a counterintuitive finding that degrading a network that is susceptible to congestion may decrease the equilibrium travel cost for each of its users. We illustrate this paradox with two networks: a basic network with four alternative routes from a single origin to a single destination, and an augmented network with six alternative routes. We construct the equilibrium solutions to these two networks, which jointly give rise to the paradox, and subject them to experimental testing. Our purpose is to test the generality of the BP when the network is enriched as well as the effects of the information provided to the network users when they conclude their travel. To this end, we compare experimentally two information conditions when each of the two networks is iterated in time. Under public monitoring each user is accurately informed of the route choices and payoffs of all the users, whereas under private monitoring she is only informed of her own payoff. Under both information conditions, over iterations of the basic and augmented games, aggregate route choices converge to equilibrium.
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Aoki K., Ohtsubo Y., Rapoport A., Saijo T. (2007) Effects of prior investment and personal responsibility in a simple network game. Current Research in Social Psychology 13(2): 10–21
Arnott R., de Palma A., Lindsey R. C. (1993) A structural model of peak-period congestion—A traffic bottleneck with elastic demand. American Economic Review 83(1): 161–179
Aumann R. J. (1992) Irrationality in game theory. In: Dasgupta P., Gale D., Hart O., Maskin E. (eds) Economic analysis of markets and games. MIT Press, Cambridge, MA, pp 214–227
Aumann R. J. (1995) Backward induction and common knowledge of rationality. Games and Economic Behavior 8(1): 6–19
Aumann R. J. (1998) On the centipede game. Games and Economic Behavior 23(1): 97–105
Borgers T., Sarin R. (2000) Naive reinforcement learning with endogenous aspirations. International Economic Review 41(4): 921–950
Braess D. (1968) Uber ein Paradoxon der Verkehrsplanung. Unternehmensforschung 12: 258–268
Camerer C. F., Ho T. (1999) Experience-weighted attraction learning in normal form games. Econometrica 67(4): 827–874
Camerer C. F., Ho T., Chong J. (2004) A cognitive hierarchy model of games. Quarterly Journal of Economics 119(3): 861–898
Cohen J. E. (1988) The counterintuitive in conflict and cooperation. American Scientist 76(6): 577–584
Cohen J. E., Kelly F. P. (1990) A paradox of congestion in a queuing network. Journal of Applied Probability 27(3): 730–734
Dafermos S., Nagurney A. (1984) On some traffic equilibrium-theory paradoxes. Transportation Research Part B—Methodological 18(2): 101–110
Fisk C., Pallottino S. (1981) Empirical-evidence for equilibrium paradoxes with implications for optimal planning strategies. Transportation Research Part A—Policy and Practice 15(3): 245–248
Frank M. (1981) The Braess Paradox. Mathematical Programming 20(3): 283–302
Friedman J. W. (1971) A non-cooperative equilibrium for supergames. Review of Economic Studies 38(113): 1–12
Kolata, G. (1990, December 25). What if they closed 42bd street and nobody Noticed? The New York Times.
Koutsoupias, E., & Papadimitriou, C. (1999). Worst-case equilibria. In STACS’99—16th annual symposium on Theoretical aspects of computer science (Vol. 1563, pp. 404–413). Springer, Berlin.
Luce R. D., Raiffa H. (1957) Games and decisions: Introduction and critical survey. Wiley, New York
Mailath G. J., Samuelson L. (2006) Repeated games and reputations: Long-run relationships. Oxford University Press, Oxford
McKelvey R. D., Palfrey T. R. (1992) An Experimental-Study of the Centipede Game. Econometrica 60(4): 803–836
Morgan J., Orzen H., Sefton M. (2009) Network architecture and traffic flows: Experiments on the Pigou–Knight–Downs and Braess Paradoxes. Games and Economic Behavior 66(1): 348–372
Murchland J. D. (1970) Braess’s Paradox of traffic flow. Transportation Research 4(4): 391–394
Pas E. I., Principio S. L. (1997) Braess’ Paradox: some new insights. Transportation Research Part B: Methodological 31(3): 265–276
Rapoport A., Kugler T., Dugar S., Gisches E. J. (2008) Braess Paradox in the laboratory: Experimental study of route choice in traffic networks with asymmetric costs. In: Kugler T., Smith J. C., Connolly T., Son Y. J. (eds) Decision modeling and behavior in complex and uncertain environments. Springer, New York, pp 309–337
Rapoport A., Kugler T., Dugar S., Gisches E. J. (2009) Choice of routes in congested traffic networks: Experimental tests of the Braess Paradox. Games and Economic Behavior 65(2): 538–571
Rapoport A., Mak V., Zwick R. (2006) Navigating congested networks with variable demand: experimental evidence. Journal of Economic Psychology 27(5): 648–666
Roughgarden T. (2005) Selfish routing and the price of anarchy. MIT Press, Cambridge, MA
Roughgarden T. (2006) On the severity of Braess’s Paradox: Designing networks for selfish users is hard. Journal of Computer and System Science 72(5): 922–953
Roughgarden T. (2007) Routing games. In: Nisan N., Roughgarden T., Tardos E., Vazirani V. V. (eds) Algorithmic game theory. Cambridge University Press, Cambridge, MA, pp 461–486
Roughgarden T., Tardos E. (2002) How bad is selfish routing?. Journal of the ACM 49(2): 236–259
Scarsini, M., & Romania, V. (2010). Repeated congestion games with bounded rationality. Working Paper.
Selten, R., Schreckenberg, M., Chmura, T., Pitz, T., Kube, S., Hafstein, S. F., Chrobok, R., et al. (2004). Experimental investigation of day-to-day route-choice behaviour and network simulations of autobahn traffic in North Rhine-Westphalia. In Human behaviour and traffic networks (pp. 1–21). Springer, Berlin.
Smith M. J. (1978) In a road network, increasing delay locally can reduce delay globally. Transportation Research 12(6): 419–422
Steinberg R., Stone R. E. (1988) The prevalence of paradoxes in transportation equilibrium problems. Transportation Science 22(4): 231–241
Steinberg R., Zangwill W. I. (1983) The prevalence of Braess’ Paradox. Transportation Science 17(3): 301–318
Taguchi A. (1982) Braess’ Paradox in a two-terminal transportation network. Journal of the Operations Research Society of Japan 25(4): 376–388
Valiant, G., & Roughgarden, T. (2006). Braess’s paradox in large random graphs. In Proceedings of the 7th ACM conference on Electronic commerce (pp. 296–305). Ann Arbor, MI: ACM.
Youn H., Gastner M.T., Jeong H. (2008) Price of anarchy in transportation networks: Efficiency and optimality control. Physical Review Letters 101(12): 128701(1)–128701(4)
Acknowledgements
This research has been supported by grant 1008393 awarded to the University of Arizona by the National Science Foundation. We thank Filippo Rossi and Maya Rosenblatt for their help in data collection.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Gisches, E.J., Rapoport, A. Degrading network capacity may improve performance: private versus public monitoring in the Braess Paradox. Theory Decis 73, 267–293 (2012). https://doi.org/10.1007/s11238-010-9237-0
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DOI: https://doi.org/10.1007/s11238-010-9237-0