Consider a Cournot competition game. The market demand function is: p= 4 – q1 – q2, - - where p is price and q is firm i's output level. Suppose that the firm's marginal cost of production is: C1 = 1, c2 = 0, respectively. A) Find the Nash equilibrium of the above game.
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- Consider the following normal form representation of the standard competition between firm A and firm B. Each firm can choose either standard A or standard B. Their payoffs are given as follows: Firm B A В A Firm A В 1 1 3 1 (1) (10 points) What's Nash equilibrium (NE) in this game? If there are more than one, find them all. But there is no NE, state that there is no NE. (2) (10 points) If you find a NE (or multiple Nash equilibria), is it (or are they) Pareto efficient?Consider a Stackelberg duopoly:There are two firms in an industry with demand Q = 1 − Pd.The “leader” chooses a quantity qL to produce. The “follower” observes qL and chooses a quantity qF.Suppose now that the cost function is Ci(qi) = qi2 for i = L, F. (a) Find the subgame perfect equilibrium. (b) Compare the equilibrium you found with the Nash equilibrium if the game was simultaneous (i.e., Cournot competition). Is the Nash equilibrium of the Cournot game also a Nash equilibrium of the sequential game? Why or why not?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. d)Now suppose instead of playing their strategies at the same time, firm A moves first and then firm B moves second(sequentialgame).Does firm A earn higher profits in this game or the game in part c)?
- 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)consider a market with inverse demand P(Q) = 10 − Q and two firms with cost curves C1(q1) = 2q1 and C2(q2) = 2q2 (that is, they have the same marginal costs and no fixed costs). They compete by choosing quantities. Now consider a modified game, which goes as follows: First, Firm 1 decides whether to enter the market or not. As in the previous question, there is no fixed cost, even if the firm decides to enter. Next, Firm 2 observes Firm 1’s entry choice and decides whether to enter or not.Firm 2 has no fixed cost as well. If no firm enters, the game ends. If only one firm enters, that firm chooses quantity, operating as a monopolist. If both firms enter, then Firm 1 chooses quantity q1. Then, Firm 2 observes Firm 1’s choice of q1 and then chooses q2 (like in the previous question). If a firm does not enter, it gets a payoff of zero. Which of the following statements is consistent with the SPNE of this game? Hint: you don’t need complicated math to solve this problem.(a) Neither firm…Consider two ice cream sellers competing at a beach that is 1000 metres long. Ice cream prices are fixed by the ice cream company, but companies can choose their locations simultaneously. Customers are located uniformly (spread out evenly on the beach) and do not like walking. The cost of walking every metre is the same (i.e. linear cost). a) Suppose there are three ice cream sellers that locate simultaneously. Find the Nash equilibrium is there is one. Else, explain why there is none. (Focus on pure strategy Nash equilibria)
- Consider an oligopoly market with 3 firms. They face a demand curve given by p(Q) = 300 – 5Q, where Pmin refers to the lowest price offered by any firm. The marginal costs are the following: C₁ = : 80, C₂ 210. The fixed costs for each firm are zero and firms compete a la Bertrand. Which of the following is consistent with a Nash equilibrium of this game? € refers to the minimal price change possible. = (a) Pmin (b) Pmin (c) Pmin (d) Pmin (e) Pmin = 80 and only firm 1 sells. 200, C3 - 190 and only firm 1 sells. = = 200 - € and only firm 1 sells. 200 and firms 1 and 2 sell. - = = 210 and all firms sell.Game Theory. Consider a Stackelberg competition game with three firms. Firm 1 chooses q1 first. Firm 2 observes q1 and chooses q2. Firm 3 observes both and chooses q3. These three firms are the only firms in the market, so the sum of their outputs is equal to total market supply, i.e. q1+q2+q3=Q. Suppose demand is given by P=12-Q. For simplicity of calculation, suppose each firm has marginal costs of 0, i.e. c1(q1)=0, c2(q2)=0 and c3(q3)=0. (1) What quantity does Firm 1 produce in the SPNE of the game? (2) What quantity does Firm 2 produce in the SPNE of the game? (3) What quantity does Firm 3 produce in the SPNE of the game?Two identical firms each have a cost function TC = 2y2 and the market demand for their output is P = -4Q+192a) Write the âbest responseâ function for each firm.b) Find the Nash equilibrium in this model c) Show that if each firm produces 1 fewer units than the result in (b), both firms make more profit. Use this information to construct a normal form game. Explain why this game is a prisonerâs dilemma.
- Let G be the following static game. Rose Colin A A (3,4) B (4,2) B (1,5) (0, 1) (a) Determine the pure Nash equilibria of G. (b) Rose A, B, Colin A, B is a mixed Nash equilibrium of H. (You do not have to verify this.) Determine the expected payoffs of both players given that they choose their strategies according to this Nash equilibrium. (c) Draw the payoff polygon of H. Indicate on your diagram the points corresponding to the Nash equilibria of H, and the points corresponding to Pareto optimal solu- tions of H.Problem 5.1. The inverse market demand for printer paper is given by P = 400 – 2Q. There are two firms who compete to produce this paper, each with a marginal cost of production equal to c = 40 over a large range of output (ie, assume constant marginal cost). The two firms compete in quantities, in other words they each simultaneously choose a quantity to produce (Cournot competition). Derive the Cournot-Nash equilibrium of this game. Please write final answers in the boxes, showing work in blank areas. (a) The reaction function for each firm. 91 (92): 92 (91) (b) Optimal output q for each firm. 92 = р = = π1 = (c) Market price (from demand curve). (d) Firm profits. 92 = π2 =Please no written by hand and no image (Bertrand's duopoly game with discrete prices) Consider the variant of the example of Bertrand's duopoly game in this section in which each firm is restricted to choose a price that is an integral number of cents. Take the monetary unit to be a cent, and assume that c is an integer and a>c+!. Is (c,c) a nash equilibrium of this game? Is there any other nash equilibrium?