Consider an industry that consists of two firms, Firm I and Firm A. The inverse demand function in this industry is p = 1 - qI - qA, and the cost functions are CI = qI and CA = qA. Suppose that Firm I is the leading firm in this industry, and hence, Firm I designsthe strategic environment, i.e., Firm I determines the game stages and the sequence of moves. The strategic environment is as follows. In Stage 1, Firm I makes a non-binding announcement about its output level. It may announce that unless Firm A produces no goods and leaves the market (thus allowing Firm I to be a monopolist), it will "flood the market" by producing an output of 1 and will therefore drive the price to zero; or, it may announce its intention to share the market with Firm A by producing an output of 4 1/6. In Stage 2, after observing Firm I's announcement, Firm A decides whether to remain in the market and produce an output of 1/6, or to leave the market. Firm A's decision is observed by Firm I. If Firm A decides to leave the market, the game ends. Otherwise, Stage 3 starts. In Stage 3, Firm I chooses its output level. It may decide to fulfill its announcement and produce and output of 1; or it may decide to produce an output of 1/6.

a.

Represent this strategic environment in an extensive form and characterize the SPNE for this game. Provide intuitive explanation regarding your results.

b. Suppose that Firm I has the ability to redesign the duopolistic market and hires you as a business consultant. Would you recommend any changes in the strategic environment? Explain.