The Algorithm of Finding Equilibrium in the Class of Fully-mixed Strategies in the Logistics Market with Big Losses

Anna A. Sergeeva, Vladimir M. Bure

St. Petersburg State University, Faculty of Applied Mathematics and Control Processes, Universitetski pr. 35, St. Petersburg, 198504, Russia

Abstract: The problem of customer optimal behavior in the service market where two service company operate to handling customer orders is considered. Each company has its own method of forming final cost of service order. The main peculiarity of considering problem is the presence of big customer losses if the lead time of fulfillment its order become very large. In this paper we formulate and prove the theorem for finding optimal strategies for players behavior when choosing a service provided with non-linearity of the loss function.

Keywords: game-theoretical approach, optimal behavior, probability modeling, construction market, nonlinear penalty, $n$ persons game, Nash equilibrium, the fully-mixed strategies.

Language: English