ABSTRACT
We apply (23) for the two-stage game instead of our quadratic congestion delay cost function (4). Solving (9) yields the best response functions of shipping lines’ port call decision at port 1:
qLi1 ¼ f g2K1 � g1K2ð Þ þ g22NK1
N � K1K2 g2 p� c� μ2ð Þ � g1 p� c� μ1ð Þf g
2a g22K1 þ g21K2
N 2 (24)
where superscript L stands for linear congestion delay cost. Based on (24) and the firstorder condition of port profit function (14), we found that Propositions 1 and 2 are satisfied. Hence, this case also guarantees the existence of a unique Nash equilibrium in port prices. The best response function of port 1 can be obtained by substituting (24) into port 1’s first-order condition (14), and solving for its price µ1.
