We investigate Cournot and Stackelberg mixed duopoly models where a stateowned public firm maximizing domestic social surplus, and a foreign firm searching to maximize its own profit, compete. First, we establish the existence and uniqueness results for the Cournot scheme, and propose the agents' classification as strong or weak according to the agent's optimal reaction function properties at the Cournot equilibrium. Then we examine a desirable role (either leader or follower) of both firms in the Stackelberg schemes and compare the profits and domestic social surplus and the production volumes at each type of Stackelberg equilibrium.

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