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Two-Player Noncooperative Games over a Freight Transportation Network

DEEI, Università degli Studi di Trieste, via A. Valerio 10, 34127 Trieste, Italy
DIC, Università degli Studi di Trieste, p.le Europa 1, 34127 Trieste, Italy
DINFO, Università degli Studi di Palermo, v.le delle Scienze, 90128 Palermo, Italy
DEEI, Università degli Studi di Trieste, via A. Valerio 10, 34127 Trieste, Italy
castelli{at}units.it
longo{at}dic.univ.trieste.it
pesenti{at}unipa.it
ukovich{at}units.it

A game between two players acting on the same road transportation network is considered in this paper. The first player aims at minimizing the transportation costs, whereas the second player aims at maximizing her profit (or, in general, her utility) that is proportional to the flow passing through the arcs under her control. We introduce bilevel linear programming formulations for this problem. We derive conditions of existence and properties of the equilibrium points and propose an algorithm finding a local optimal solution. Finally, we present an application of the model to a real system involving trucks travelling through Europe from a Middle Eastern country.

Key Words: freight transportation; noncooperative games; networks; bilevel programming
History: Received: November 2000; revised: June 2001; revised: January 2002; accepted: April 2002.