Bargaining between the host country and oil companies is very common to international oil and gas development projects. The existence of information asymmetry gives the host country an endogenous bargaining advantage. Foreign oil companies might change their unfavorable negotiating position by changing the order of bidding and adjusting bidding strategies. This paper introduces both factors into a bilateral bargaining model to study the impact of information asymmetry and bidding order on the strategy and equilibrium returns of oil companies. According to the ownership of the right to bid first, two scenarios are designed for the model to compare the equilibrium returns of the host country and oil companies. The results show that: 1) There is a first-mover advantage in the process of bilateral bidding, so oil companies better bid first; 2) The information asymmetry will lead to a higher nominal income ratio of oil companies and a lower nominal income ratio of the host country, but it doesn't affect the total income ratio at all.