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An Evolutionary Approach to Congestion

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  • William H. Sandholm
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    Abstract

    Using techniques from evolutionary game theory, we analyze potential games with continuous player sets, a class of games which includes a general model of network congestion as a special case. We concisely characterize both the complete set of Nash equilibria and the set of equilibria which are robust against small disturbances of aggregate behavior. We provide a strong evolutionary justification of why equilibria must arise. We characterize situations in which stable equilibria are socially efficient, and show that in such cases, evolution always increases aggregate efficiency. Applying these results, we construct a parameterized class of congestion tolls under which evolution yields socially optimal play. Finally, we characterize potential games with continuous player sets by establishing that a generalization of these games is precisely the limiting version of finite player potential games (Monderer and Shapley (1996)) which satisfy an anonymity condition.

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    Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1198.

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    Date of creation: Apr 1997
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    Handle: RePEc:nwu:cmsems:1198

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    1. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    2. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
    3. Ritzberger, Klaus & Weibull, J├Ârgen W., 1993. "Evolutionary Selection in Normal Form Games," Working Paper Series 383, Research Institute of Industrial Economics.
    4. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer, vol. 19(1), pages 59-89.
    5. Pas, Eric I. & Principio, Shari L., 1997. "Braess' paradox: Some new insights," Transportation Research Part B: Methodological, Elsevier, vol. 31(3), pages 265-276, June.
    6. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
    7. Binmore, K. & Samuelson, L., 1997. "Evolutionary Drift and Equilibrium Selection," Working papers 9729r, Wisconsin Madison - Social Systems.
    8. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    9. Richard Arnott & Kenneth Small, 1993. "The Economics Of Traffic Congestion," Boston College Working Papers in Economics 256, Boston College Department of Economics.
    10. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
    11. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
    12. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
    13. A. Gaunersdorfer & J. Hofbauer, 2010. "Fictitious Play, Shapley Polygons and the Replicator Equation," Levine's Working Paper Archive 438, David K. Levine.
    14. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October.
    15. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May.
    16. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May.
    17. Jeroen M. Swinkels, 1991. "Adjustment Dynamics and Rational Play in Games," Discussion Papers 1001, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    18. Barro, Robert J & Romer, Paul M, 1987. "Ski-Lift Pricing, with Applications to Labor and Other," American Economic Review, American Economic Association, vol. 77(5), pages 875-90, December.
    19. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
    20. Friedman, Eric J., 1996. "Dynamics and Rationality in Ordered Externality Games," Games and Economic Behavior, Elsevier, vol. 16(1), pages 65-76, September.
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