This paper develops a two stage game model with two competing firms in a mixed oligopolistic market, a public firm and a private firm, and only the public firm giving its manager an incentive contract. The paper presents three types of public firm owner’s objective function and each objective function corresponds to three types of delegation, either of a profit-revenue type, or of a relative performance, or, finally, of a market share one. In an equilibrium, the public firm owner has a dominant strategy to reward his manager with an incentive contract combining own profits and competitor’s profits. Different from Manasakis et al. (2007), this paper suggests that the dominant strategy of the public firm owner is to reward his manager with a profit-revenue type of contract or a market-share type of contract, that is to say profit-revenue is identical with market-share. Using relative-performance type of contract will move the manager away from the owner’s true objective function when the public firm owner only pursues maximizing the social welfare. The private firm will be crowded out and the public firm is the only producer of the market. Under profits-revenues type of contract, the owner’s objective of maximizing the summation of the profit and consumer surplus leads the manager more aggressive. Different combinations give us different results. By comparing the results, each type of incentive contract is an owner’s best response to his decision.