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An Evolutionary Approach to Congestion

  • William H. Sandholm
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    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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    File URL: http://www.kellogg.northwestern.edu/research/math/papers/1198.pdf
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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
    Contact details of provider: Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
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    Web page: http://www.kellogg.northwestern.edu/research/math/
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    1. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
    2. 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.
    3. Samuelson, L. & Zhang, J., 1990. "Evolutionary Stability In Symmetric Games," Working papers 90-24, Wisconsin Madison - Social Systems.
    4. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-99, November.
    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. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
    7. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, June.
    8. 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.
    9. Binmore, K. & Samuelson, L., 1997. "Evolutionary Drift and Equilibrium Selection," Working papers 9729r, Wisconsin Madison - Social Systems.
    10. Swinkels Jeroen M., 1993. "Adjustment Dynamics and Rational Play in Games," Games and Economic Behavior, Elsevier, vol. 5(3), pages 455-484, July.
    11. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    12. 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.
    13. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November.
    14. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
    15. 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.
    16. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May.
    17. Richard Arnott & Kenneth Small, 1993. "The Economics Of Traffic Congestion," Boston College Working Papers in Economics 256, Boston College Department of Economics.
    18. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
    19. Friedman, Eric J., 1996. "Dynamics and Rationality in Ordered Externality Games," Games and Economic Behavior, Elsevier, vol. 16(1), pages 65-76, September.
    20. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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