Nash bargaining of transportation rates with flow imbalances

Abstract

Consider two points, A and B, which trade products with a flow imbalance. We postulate that shippers at A face an implicit negotiation with the shippers at B regarding who must bear the cost of a vehicle travelling back and forth. Following the Nash bargaining model, we deduce that the ratio (freight rate A-to-B)/(freight rate B-to-A) changes linearly with the ratio (flow B-to-A)/(flow A-to-B). We validate our model with evidence from previous publications and with quarterly data from the Transatlantic, Transpacific and Europe-Asia maritime routes from 2003 to 2012.