THE PRICE OF ANARCHY IN AN UNCAPACITATED DETERMINISTIC SHIPMENT CONSOLIDATION GAME

Collaboration of companies for logistics activities result in more efficient use of logistics resources which leads to reduction of logistic costs. In this study, multiple shippers that make shipments from the same origin to the same destination are under consideration. The shipment requests of the shippers arrive over time at a deterministic uniform constant rate and the shippers consolidate their shipments on uncapacitated trucks. The trucks are dispatched at a certain frequency to maximize the profit gained from the shipments. Two settings are analyzed, where in the first shippers act as a coalition, and in the second, each of these shippers acts selfishly. The former is analyzed under a cooperative game while the latter under a non-cooperative Nash game. For the cooperative game the structure of the characteristic function is analyzed and the properties such as monotonicity, superadditivity, core existence and convexity are shown. For the non-cooperative game the conditions under which the Nash equilibrium exists are identified. Through numerical analysis the price of anarchy and the Gini coefficient are quantified by comparing the total profit and average individual profit of each shipper under cooperative and non-cooperative games.