Alternating Offers Bargaining Game and Wardrop's User Equilibrium

Nash의 협상게임과 Wardrop의 사용자 균형

  • 임용택 (여수대학교 교통물류시스템공학부)
  • Published : 2005.09.06

Abstract

This paper presents a relationship between Nash bargaining game and Wardrop user equilibrium, which has been widely used in transportation modeling for route choice problem. Wardrop user equilibrium assumes that drivers in road network have perfect information on the traffic conditions and they choose their optimal paths without cooperation each other. In this regards, if the bargaining game process is introduced in route choice modeling, we may avoid the strong assumptions to some extent. For such purpose, this paper derives a theorem that Nash bargaining solution is equivalent to Wardrop user equilibrium as the barging process continues and prove it with some numerical examples. The model is formulated based on two-person bargaining game. and n-person game is remained for next work.

References

  1. 박순달(1992), 게임이론, 민영사
  2. 임용택. 임강원(2004), Bi-level program에서 Cournot-Nash게임과 Stackelberg게임의 비교연구, 대한교통학회지, 제22권 제7호, 대한교통학회, pp.99-106
  3. 최기주. 장정아(2004), 게임이론에 기반한 VMS 운영모형, 대한토목학회논문집, 제24권 제2D호, 대한토목학회, pp.155-165
  4. Altman, E., L. Wynter(2004), Equilibrium, games, and pricing in transportation and telecommunications networks, Networks and Spatial Economics 4, pp. 7-21 https://doi.org/10.1023/B:NETS.0000015653.52983.61
  5. Altman. E., T. Boulogne. R. El-Azouzi, T. Jimenez, L. Wynter(2005), A survey on networking games in telecommunications, Computers & Operations Research. in press
  6. Bell, M. G. H., Chris Cassir(2002), Risk-averse user equilibrium traffic assignment: an application of game theory, Transportation Research 36B. pp.671 -681 https://doi.org/10.1016/S0191-2615(01)00022-4
  7. Dafermos, S., Sparrow, F. T.(1968), The traffic assignment problem for a general network, Nastional Bureau of Standards. J. Res. 73B, pp.91-118.
  8. Fisk, C. S.(1984), Game theory and transportation systems modelling, Transportation Research Vol. 18B, pp.301-313 https://doi.org/10.1016/0191-2615(84)90013-4
  9. Harker. P. T.(1991), Generalized Nash games and quasi-variational inequalities. European Journal of Operational Research 54. pp.81-94 https://doi.org/10.1016/0377-2217(91)90325-P
  10. Kalai, E., M. Smorodinsky(1975). Other solutions to Nash's bargaining problem. Econometrica 43. pp.513-518 https://doi.org/10.2307/1914280
  11. Nash. J.(1950). The bargaining problem, Econometrica 18. pp.155-162 https://doi.org/10.2307/1907266
  12. Nash. J.(1951). Noncooperative games. Ann. Mathematics 54. pp.286-295 https://doi.org/10.2307/1969529
  13. Nash. J.(1953). Two-person cooperative games, Econometrica 21, pp.128-140 https://doi.org/10.2307/1906951
  14. Naeve-Steinweg, E.(2004), The averaging mechanism, Games and Economic Behavior 46, pp,410-424 https://doi.org/10.1016/S0899-8256(03)00123-4
  15. Rocheteau. G., C. Waller(2004), Bargaining in monetary economies, Australian National University, working paper
  16. Rosenthal. R. W.(1973), The network equilibrium problem in integers, Networks 3, pp.53-59 https://doi.org/10.1002/net.3230030104
  17. Rubinstein, A.(1982), Perfect equilibrium in a bargaining model, Econometrica 50, pp.97-109 https://doi.org/10.2307/1912531
  18. Smith. M. J.(1979), The existence, uniqueness and stability of traffic equilibria, Transportation Research 13B, pp.295-304 https://doi.org/10.1016/0191-2615(79)90022-5
  19. Wardrop J. G.(1952), Some theoretical aspects of road traffic research, Proc. Inst. Civil Engineer, Part II, pp.325-378
  20. Weber. R.(2003), Mathematics for operation research, M. Phil in Statistical Science, Mathematical Tripos, Part III
  21. Zhou. J., W. H. K. Lam, B. G. Heydecker (2005), The generalized Nash equilibrium model for oligopolistic transit market with elastic demand, Transportation Research 39B, pp.519-544 https://doi.org/10.1016/j.trb.2004.07.003