1. Consider the Cournot Duopoly model with inverse demand: _ abQ inga P(Q)_{0 ifQ>a where a,b > 0, and costs of production c,;(qz-) = cqz- for each rm. Assume a > c 2 0. a. Write the payoffs (prots) of each rm and describe the game formally (i.e., identify the 3 elements which dene a game) b. Write the maximization problem of each rm and obtain their best response correspondences. What is the impact of an increase of rm 2 production on the optimal production decision of rm 1? c. Compute the prots each rm is obtaining in equilibrium and the price at which each unit is sold in equilibrium. 2. Consider the game described in the matrix below where 3:, y, and z are real numbers. a. For which values of 513,3}, z is (U, L) a Nash equilibrium? b. For which values of :12, y, z is (D, R) a Nash equilibrium? c. For which values of 56,11, z is (D, L) a Nash equilibrium