Assume that generators 1 and 2 have asymmetric strategies in a duopolistic bidding. Generator 2 adjusts its current strategy according to marginal profit of the last period; Generator 1 selects optimal strategy so as to maximize its objective during a given time period subjected to a dynamic constraint from generator 2's strategy. This paper uses optimal control to analyze the effect of cost and demand on generator 1's excessive profit. The main result is that, if the marginal cost increases very fast and the market demand is very elastic, then equilibrium strategy in the steady state converges to the static Cournot case. This implies that, the player with dominant information cannot improve its profit significantly.