2 firms are engaged in Cournot competition; firm A faces the cost curveCA(yA)=40yAand firm Bfaces the cost curveCB(yB)=40yB. The inverse market demand curve isP(y)=100y, whereyrepresents market level of output.   a)Define the Cournot game.   b)In 1 or 2 sentences explain why a firm has no incentive to deviate from the Cournot Nash equilibrium(holding their opponent’s strategy constant).        c)Find the Cournot Nash Equilibrium.

For problem 1 and 2, consider the following game : с D A (0,5) (5,-5) B (3, 1) (1, 0) 1. Show that the game above doesn't have a pure Nash equilibrium. 2. Show that the game above has a unique mixed Nash equilibrium, and describe the playing strategy.

(J)

Problem 3. Consider the following game with three firms. First, firms 1 and 2 si- multancously choose quantities q1 and q2 respectively. After observing firm 1 and 2's quantities, firm 3 chooses its quantity q3. There is no production cost and the inverse demand function is p= 12 – (91 +2 + 93). (a) Compute the SPNE of this game. (b) Give an example of Nash equilibrium s* with s = 4 and s, = 6 , that is not subgame perfect. game theory question

am. 116.

What are the sub games in the following game? Find all subgame perfect Nash equilibria (SPNE)

Find Nash equilibrium using cell by cell inspection

4

O Cell A O Cell C O Cell E O Cell I None of the above

Consider the game in the table below. Find the Nash Equilibrium of the game. Add the payoffs of both players at the Nash Equilibrum and enter that number. Firm A Left Right Up Firm B 9,11 5,6 own 5,10 6,5 20