Investment in the future consider two firms that play a, Management Theories

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Investment in the future consider two firms that play a

Investment in the Future: Consider two firms that play a Cournot competition game with demand p = 100 - q and costs for each firm given by c_i(q_i) = 10q_i. Imagine that before the two firms play the Cournot game firm 1 can invest in cost reduction. If it invests the costs of firm 1 will drop to c₁(q₁) = 5q₁. The cost of investment is F > 0. Firm 2 does not have this investment opportunity.

a. Find the value F∗ for which the unique subgame-perfect equilibrium involves firm 1 investing.

b. Assume that F>F∗. Find a Nash equilibrium of the game that is not subgame perfect.

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Management Theories: Investment in the future consider two firms that play a

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