Algorithm for determing equilibrium provided penalties for delay in the construction market

V. M. Bure ; A. A. Sergeeva

Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2013), pp. 32-38

Résumé

The construction market with three company contractors is considered. Customers in the market are construction companies. They select a contractor to perform the work trying to minimize the total cost of service. Two providers are service companies in the construction market which provide repairs and cosmetic finishing works for clients. Each of provider has its own scheme of customer order fulfillment and own cost policy. An important feature of the problem is the possibility of the client to incur heavy costs if the duration of work exceeds a certain pre-defined limit. We consider the optimal choice of the client in terms of cost minimization. Costs consist of direct client costs orders for the scheme which is set by the provider specific losses and penalties which are charged to the client for delay in work delivery. In this case under penalty extra money is meant that is paid to the contractor if the nature of the work is too difficult. Each contractor shall determine its own policy formation of the final price. Costs consist of fixed clients and temporary component. There is introduced the class of fully-mixed strategies. The theorem which determine points of Nash equilibrium under three possible cases is formulated and proved. The optimal behavior of customers in terms of fully-mixed strategies is found. Bibliogr. 5.

Détail

Keywords: probability modeling, game-theoretical approach, construction market, big penalties, nonlinear penalty, $n$-person game, Nash equilibrium, fully-mixed strategies.