Consider a Stackelberg game of quantity competition between two firms. Firm 1 is the leader and firm 2 is the follower. Market demand is described by the inverse demand function P=1000-4Q. Each firm has a constant unit cost of production equal to 20. Suppose firm 2's unit cost of production is c<20. What value would c have so that in the Nash Equilibrium, the two firms, the leader and the follower, had the same market share?

Two firms X and Y compete with each other. Firm X can produce one of three products X1, X2, or X3. Similarly, firm Y can produce one of three products Y1, Y1, and Y3. Each firm's profit depends on its own and its competitor's decision about which product to produce. These profits are given in the table below where each cell presents profits corresponding to a pair of chosen strategies with the first number being the profit of firm X and the second being the profit of firm Y. For example, if X chooses to produce X3 and Y chooses to produce Y1, the profit of X will be $15 and the profit of Y will be $20. The firms make their product choice decisions simultaneously and independently of each other. Y1 Y2 Y3 X1 0, 0 12, 8 16, 16 15, 20 18, 9 20, 15 8, 12 18, 18 9, 18 X2 X3 11) Does this game have any equilibrium in dominant strategies? If yes, find all of them. 12) In addition to the equilibria (if any) you found in the previous question, does this game have any other equilibria? If yes,…

We can see from the payoff matrix that there are no pure strategy Nash equilibrium in this game because at least one firm would always have an incentive to change its behavior. ​ From​ Nash's​ theorem, we know there must be at least one Nash equilibrium so there must be a mixed strategy Nash equilibrium for this game.   Find the mixed strategy Nash equilibrium by first deleting all dominated strategies in the game   What's the expected payoff to Firm 1 in the equilibrium?

Suppose two firms A and B compete against each other in a Cournot fashion by choosing their quantities. What is the Nash Equilibrium of the game if both firms have a constant marginal cost of 2 and the price in the market is: p(qa + qB) = 20 – 2(qA + qB). O (3, 3) O (2, 2) O (4, 4) None of the other answers are correct (5, 5)