Cournot model: linear demand; identical firms. Q(P)=D-P TC(C)=cQ, where D>c a) Suppose that there are 2 firms. They can either choose to produce the Cournot quantity, or choose to produce one half of the monopoly quantity. Write down the 2X2 “payoff matrix” for this game. b) If D= 6 and c = 2, suppose that the game is repeated infinitely often with a discount factor of beta. For what values of beta will it be possible to sustain collusion? c)  Now consider the same game with 3 firms. Compute the profits in the static Cournot- Nash equilibrium, and the profits when the 3 firms each produce one third of the monopoly quantity. For what values of beta will it be possible to sustain collusion in this case?

I have constructed a Bertrand game (competition in prices) and presented you with the reaction functions of each firm. p1 = 12.5 + p2/4 p2 = 5/2 + p1/2   a) Use excel to draw the reaction functions. b) Solve for the Nash equilibrium

where is the nash equilibrium? find out the dominant strategy. it was discovered that two domestic manufacturing companies were fixing prices. if each company is silent, there is no penalty, but production and business are disrupted due to continuous investigation by the Fair Trade Commission. The penalty for revealing the estimated loss due to the investigation and collusion is as follows:                                            Firm 2                             Silence                 Disclosure      Silence            -200, -200            -590, 0      Firm 1 Disclosure            0, -590                  -450, -450            fine( a hundred million won)

Assume the following scenarios. First, identify their nature of the situation (that is, which type of game and situation is implied) and second, discuss each one of them in terms of outcomes and possible solutions. (a) A cartel has a collective interest in restricting output to earn a monopoly profit. At the same time, cartel members can increase their individual profits by cheating on the cartel, that is, exceeding their quotas. (b) Abnormally cold winter temperatures bring the threat of a shortage of natural gas for heating buildings and homes.

Consider a game where a potential market Entrant is trying to decide whether or not to enter the market. An Incumbent monopolist is established and can choose to cut the price, maintain the price, or raise the price in hopes of deterring the Entrant from entering. Incumbent Entrant Enter Stay Out Cut Price -4,4 0,9 Maintain Price 4,6 0,12 Raise Price 5,5 0, 13 a) Suppose the Entrant and the Incumbent make their decisions simultaneously. Is there a pure strategy Nash equilibrium? If so, what is it? b) Suppose the players move sequentially, and that the Entrant moves first. Set up the game tree and solve for the equilibrium path. Can the Incumbent deter entry? Explain. c) Now suppose that the Incumbent moves first. Again, set up the game tree. What is the subgame perfect Nash equilibrium outcome now? Can the Incumbent deter entry now?

Consider a duopoly market, where two firms sell differentiated products, which are imperfect substitutes. The market can be modelled as a static price competition game, similar to a linear city model. The two firms choose prices p, and p2 simultaneously. The derived demand functions for the two firms are: D1 (P1, P2) = SG+P1)and D2 (P1, P2)= S(;+-P2), where S > 0 and the parameter t > 0 measures the 2t 2t degree of product differentiation. Both firms have constant marginal cost c> 0 for production. (a) Derive the Nash equilibrium of this game, including the prices, outputs and profit of the two firms. (b) From the demand functions, qi= D¡ (p; , p¡ )= SG+P), derive the residual inverse demand functions: p; = P; (qi , p¡) (work out: P; (qi , P;)). Show that for t > 0, P;(qi , P;) is downward 2t aPi (qi ,Pj) . sloping, i.e., c, i.e., firm į has market power. %3D (c) Calculate the limits of the equilibrium prices and profit as t → 0 ? What is P; (qi , p;) as t → 0? Is it downward sloping?…

QUESTION 13 Consider a market where two firms (1 and 2) produce differentiated goods and compete in prices. The demand for firm 1 is given by D₁(P₁, P2) = 140 - 2p1 + P2 and demand for firm 2's product is D2 (P1, P2) 140 - 2p2 + P1 Both firms have a constant marginal cost of 20. What is the Nash equilibrium price of firm 1? (Only give a full number; if necessary, round to the lower integer; no dollar sign.)

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?

I have constructed a Bertrand game (competition in prices) and presented you with the reaction functions of each firm. P2 P1 = 12.5 + 4 P1 P2 == Use excel to draw the reaction functions. Solve for the Nash equilibrium + n IN

Two firms are engaged in duopoly competition in a market with demand Q = 120 - p and zero costs.   The reaction function for firm i given firm j's output q i = 60 - 1 2 q j .   What is the payoff to firm i if the two firms engaged in collusion to maintain monopoly output and prices. Assume that each firm gets half the monopoly profit.