Volume 15, No 3, 2008, P. 31-42

UDC 519.833.2, 519.8:656
V. I. Zorkaltsev, M. A. Kiseleva
Nash equilibrium in transport model with quadratic costs

Abstract:
The paper deals with the problem of coordinating the plans on conveyance of several clients by a single transport system at the conveyance tariffs of the separate arcs those are linearly dependent on the total conveyance volumes at these arcs. In this case the conveyance costs at separate arcs for every client are quadratic functions of this client conveyance volume when other clients conveyance volumes are fixed. The existence and uniqueness of the Nash equilibrium are proved. It is shown that the problem of finding a Nash equilibrium for concerned nonlinear transport problem leads to solving a quadratic programming problem. 
Bibl. 5.

Keywords: nonlinear transport model, Nash equilibrium.

Zorkalsev Valery Ivanovich ¹
Kiseleva Marina Alexandrovna ¹
1. Melentiev Institute of Energy Systems, SB RAS,
Lermontov str., 130, 664033 Irkutsk, Russia
e-mail: zork@isem.sei.irk.ru, marinee@mail.ru