Repeated Commuting

Berliant, Marcus (2011): Repeated Commuting.

Abstract

We examine commuting in a game-theoretic setting with a continuum of commuters. Commuters' home and work locations can be heterogeneous. The exogenous transport network is arbitrary. Traffic speed is determined by link capacity and by local congestion at a time and place along a link, where local congestion at a time and place is endogenous. After formulating a static model, where consumers choose only routes to work, and a dynamic model, where they also choose departure times, we describe and examine existence of Nash equilibrium in both models and show that they differ, so the static model is not a steady state representation of the dynamic model. Then it is shown via the folk theorem that for sufficiently large discount factors the repeated dynamic model has as equilibrium any strategy that is achievable in the one shot game with choice of departure times, including the efficient ones. A similar result holds for the static model. Our results pose a challenge to congestion pricing. Finally, we examine evidence from St. Louis to determine what equilibrium strategies are actually played in the repeated commuting game.

• Item Type: MPRA Paper
• Language: English
• Keywords: commuting; folk theorem
• Subjects: R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R4 - Transportation Economics > R41 - Transportation: Demand, Supply, and Congestion ; Travel Time ; Safety and Accidents ; Transportation Noise

References

Anas, A., 2007. "The Trips-to-Flows Riddle in Static Traffic Equilibrium: How to drive a BMW ?" Unpublished manuscript.

Arnott, R., A. de Palma and R. Lindsey, 1993. "A Structural Model of Peak-Period Congestion: A Traffic Bottleneck with Elastic Demand." American Economic Review 83, 161-179.

Beckmann, M., C.B. McGuire and C.B. Winsten, 1956. Studies in the Economics of Transportation. Yale University Press: New Haven.

Braess, D., 1968. "Uber ein Paradoxonder Verkehrsplanung." Unternehmensforschung 12, 258-268.

Chung, J.W., 1979. "The Nature of Substitution Between Transport Modes." Atlantic Economic Journal 7, 40-45.

Daganzo, C.F., 2008. Fundamentals of Transportation and Traffic Operations. Emerald Group Publishing: Bingley, UK.

Daniel, T.E., E.J. Gisches and A. Rapoport, 2009. "Departure Times in Y-Shaped Traffic Networks with Multiple Bottlenecks." American Economic Review 99, 2149-2176.

Hu, D., 2010. "Equilibrium and Dynamics of the Discrete Corridor Problem." Unpublished manuscript.

Kaneko, M., 1982. "Some Remarks on the Folk Theorem in Game Theory." Mathematical Social Sciences 3, 281-290.

Konishi, H., 2004. "Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous Commuters." Transportation Science 38, 315-330.

Lee, I.K., 1999. "Non-Cooperative Tacit Collusion, Complementary Bidding and Incumbency Premium." Review of Industrial Organization 15, 115-134.

Massó, J., 1993. "Undiscounted Equilibrium Payoffs of Repeated Games with a Continuum of Players." Journal of Mathematical Economics 22, 243-264.

Massó, J., and R.W. Rosenthal, 1989. "More on the `Anti-Folk Theorem'." Journal of Mathematical Economics 18, 281-290.

Rosenthal, R.W., 1973. "A Class of Games Possessing Pure-Strategy Nash Equilibria." International Journal of Game Theory 2, 65-67.

Ross, S.L. and J. Yinger, 2000. "Timing Equilibria in an Urban Model with Congestion." Journal of Urban Economics 47, 390-413.

Rudin, W., 1974. Real and Complex Analysis. McGraw-Hill: NY.

Sandholm, W.H., 2001. "Potential Games with Continuous Player Sets." Journal of Economic Theory 97, 81-108.

Schmeidler, D., 1973. "Equilibrium Points of Non-Atomic Games." Journal of Statistical Physics 7, 295-301.

Vickrey, W., 1963. "Pricing in Urban and Suburban Transport." American Economic Review 53, 452-465.

Vickrey, W., 1969. "Congestion Theory and Transport Investment." American Economic Review 59, 251-261.