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# 55 - ECON 3600 Assignment 5 Due Thursday March 7th Dynamic...

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ECON 3600 Assignment 5 Due Thursday, March 7th. Dynamic Games (Problems 1 and 2 adapted from Bierman and Fernandez. Problem 3 from Yale Open Course.) 1. Solve the following three-player game using backwards induction: Players are A, B, and C. Payoffs are written as (A's payoff, B's payoff, C's payoff) Solution: (1,2,2) is the BI solution. 2. Stackelberg Competition Two firms are competing over quantities. There is no cost of production and the product is exactly the same whether purchased from Firm 1 or Firm 2. The market demand is: Market Price = 10 (Q 1 +Q 2 ) a. Assume both firms choose their output quantities simultaneously. Find the Nash equilibrium price and output. Show your work. Firm 1's profit function is: ( 10 (Q 1 +Q 2 ))Q 1 . FOC: 10 - 2Q 1 - Q 2 = 0 BR 1 (Q 2 ) = (10 - Q 2 )/2 C B A (2, 1, 0) (1, 2, 2) (0, 100, 100) (100, 100,-1)

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since the game is symmetric, setting Q 1 = Q 2 gives us: Q 1 * = Q 2 *= 3.33. And P = 3.33. b. Assume the game is sequential: Firm 1 chooses its output quantity first, then Firm 2 chooses
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55 - ECON 3600 Assignment 5 Due Thursday March 7th Dynamic...

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