Container terminal concessions: A game theory application to the case of the ports of Pakistan

The objective of this article is to analyse the effect of the type of concession contracts on port user surplus and on profits of terminal operators (or port authorities) with the help of game theory. We have selected three ports in Pakistan to perform this analysis. These ports function as 'landlords' and have signed concession contracts with private container terminal operators. However, the features of the contracts at present are different for each terminal. We analyse four cases in this article. The first case is the present situation in which we treat competition between terminals as a Bertrand game in which each terminal non-cooperatively determines charges for container handling and pays fees to port authorities according to the contract. The Bertrand model seems to reproduce, to a satisfactory degree, the market shares and handling fees observed. Furthermore, in the second and third cases, a cost-benefit analysis is conducted by solving the Bertrand model. The results reveal that in the long run it is profitable for the Karachi Port to establish a same fixed fee contract with its private terminals. However, users are better off in a situation where a percentage fee concession contract would be adopted instead. The game theoretic framework is then extended to the analysis of the strategic decision faced by port authorities with respect to the trade-off between unit fees and annual rent in the last case. An optimal concession contract is obtained that is feasible for both parties in the sense that it contains high unit fees (variable cost) and low annual rent (fixed cost).