Can you suggest a better game theory than Cournot, Stackelberg and Bertrand? The Cournot Model: what happens when two firms compete simultaneously on the quantity of output they produce of a homogeneous good. The Stackelberg Model: what happens when two firms compete sequentially on the quantity of output they produce of a homogeneous good. The Bertrand Model: what happens when two firms compete simultaneously on the price of a homogenous good.
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Can you suggest a better
The Cournot Model: what happens when two firms compete simultaneously on the quantity of output they produce of a homogeneous good.
The Stackelberg Model: what happens when two firms compete sequentially on the quantity of output they produce of a homogeneous good.
The Bertrand Model: what happens when two firms compete simultaneously on the price of a homogenous good.
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- Consider two firms choosing quantities sequentially in a duopoly setting (i.e. the Stackelberg game). The two firms have identical products. Each firm has no fixed costs, and faces marginal costs equal to 5 plus the quantity it produces (i.e. MC = 5 + q). Market demand is given by Q = 46 - P, where Q is market quantity and P is market price. In equilibrium, how much will the firm that moves first produce?Three firms compete in the style of Cournot. The inverse demand is P(Q) = a - Q. Scenario 1: All three firms have the same constant marginal cost MC = c. Scenario 2: Firm 1 has MC = 0.5c, Firm 2 has MC = c, and Firm 3 has MC = 1.5c. Assume that a > 3c. Which of the following is correct? (Price means the price in Nash equilibrium.) Price in scenario 1 > Price in scenario 2 Price in scenario 2 > Price in scenario 1 Price in scenario 1 = Price in scenario 2 Any of the first three options is possible depending on the value of a Any of the first three options is possible depending on the value of a and c.Fill in the chart attached and answer the following questions: a) Bert's dominant strategy is to: (pick the correct answer below ) - no dominant strategy - fish for 20 hours per week -fish for 40 hours per week. b) Ernie's dominant strategy is to: ( pick the correct answer below) - no dominant strategy - fish for 20 hours per week -fish for 40 hours per week. c) Is there a Nash Equilibrium? ( pick the correct answer below) - No - Yes, both fish for 20 hours per week - Yes, one fisher for 40 and the other for 20. - Yes both fish for 30 hours per week. d) Is there an incentive for Bert and Ernie to collude? Why or why not?
- The New York Times reports that Wal-Mart has decided to challenge Netflix and enter the online DVD-by-mail market. Because of economies of scale, Wal-Mart has a slight cost advantage relative to Netflix. Wal-Mart is considering the use of a limit pricing strategy. It can enter the market by matching Netflix on price. If it does, and Netflix maintains its price, then both firms would earn $5 million. But if Netflix drops its price in response, Wal-Mart would have to follow and would earn $2 million; Netflix would earn $3 million. Or Wal-Mart could enter the market with a price that is below Netflix's current price but above its marginal cost. If it does, Netflix would make one of two moves. It could reduce its price to below that of Wal-Mart. If it does, Wal-Mart will earn a profit of $0, and Netflix will earn a profit of $2 mil- lion. Or Netflix could keep its present price. If Netflix keeps its present price, Wal-Mart can keep its present price and earn $6 million (while Netflix earns…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 =Consider a market with two firms, Target and Wal-Mart, that sell CDs in their music department. Both stores must choose whether to charge a high price ($25) or a low price ($17) for the new Miley Cyrus CD These price strategies with corresponding profits are depicted in the payoff matrix to the right Target's profits are in red and Wal Mart's are in blue Targefs dominant stratogy is to pick a price of s Wal Mart's dominant strategy is to pick a price of What is the Nash oquilbrium for this game? A A Nash oquilbrium does not exist for thes game OB. The Nash equilibrium is for Target to choose a price of $25 and Wal-Mart to choose a price of $17 OC The Nash oquilibrium is for Target and Wal-Mart to both choose a price of $17. The Nashi oquilbrium is for Target and Wal-Mart to bolth choose a price of $25 OE The Nash equilibrium is for Target to choose a price of $17 and Wal-Mart to choose a price of $25.
- Two firms operating in the same market must decide between charging a high price or a low price. The Payoffs are as below. Firm A's profit is listed before the comma, B's profit after the comma. Firm B Firm A Low Price High Price Low Price 16, 17 7, 28 High Price 28, 7 22, 22 If each firm tries to choose a price that is optimal, regardless of the other firm's price, what is the Nash equilibrium? Does either firm have a dominant strategy?Using a payoff matrix to determine the equilibrium outcome Suppose there are only two firms that sell smart phones, Flashfone and Pictech. The following payoff matrix shows the profit (in millions of dollars) each company will earn, depending on whether it sets a high or low price for its phones. Pictech Pricing High Low Flashfone Pricing High 11, 11 2, 18 Low 18, 2 10, 10 For example, the lower, left cell shows that if Flashfone prices low and Pictech prices high, Flashfone will earn a profit of $18 million and Pictech will earn a profit of $2 million. Assume this is a simultaneous game and that Flashfone and Pictech are both profit-maximizing firms. If Flashfone prices high, Pictech will make more profit if it chooses a ______ price, and if Flashfone prices low, Pictech will make more profit if it chooses a _____ price. If Pictech prices high, Flashfone will make more profit if it chooses a _____ price, and if Pictech prices low, Flashfone will make more…Assume that Acme and Gamma are the two main rivals in the market for hair dryers. Each firm is considering prices of $50 or $60, with the following possible profit outcomes: Gamma Price = 50 Price = 60 Price = 50 40, 45 45, 42 Acme Price = 60 24, 55 30, 48 A) Assume the firms choose prices simultaneously. Does the game have a solution? Explain. B) Is the solution you have identified a Nash Equilibrium? Explain why or why not.
- Joe and Rebecca are small-town ready-mix concrete duopolists. The market demand function is Qd = 10,000 – 100P, where P is the price of a cubic yard of concrete and Qd is the number of cubic yards demanded per year. Marginal cost is $25 per cubic yard. Suppose that Joe and Rebecca compete in quantities and competition in this market is described by Cournot model. What are Joe and Rebecca’s Nash equilibrium outputs? What is the resulting price? What do they each earn as profit? How does the price compare to the marginal cost? Joe and Rebecca are small-town ready-mix concrete duopolists. The market demand function is Qd = 10,000 – 100P, where P is the price of a cubic yard of concrete and Qd is the number of cubic yards demanded per year. Marginal cost is $25 per cubic yard. Suppose that Joe and Rebecca compete in quantities and competition in this market is described by Cournot model. What are Joe and Rebecca’s Nash equilibrium outputs? What is the resulting price? What do they each…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?Consider two firms with a homogeneous product who face the market demand function p = 2 – q1 – 92, where q; and p are the quantities and price. Their constant marginal costs are given by c= 1. The firms compete in quantities in a simultaneous move game. Use this specific example (not a general case) to show that the Nash equilibrium is not Pareto efficient, and the cooperative solution is not an equilibrium (in the sense that both firms have an incentive to cheat). In your answer, use the fact that the firms are identical. Namely, they produce equal amounts (both in the simultaneous move game and in the cooperative case).
