Two firms compete as a Stackelberg duopoly. The demand they face is P = 402 - Q. The cost function for firm 1 (the leader) is Ci(Q) = 201, and the cost function for firm 2 (the follower) is C2(Q2) = 6Q2 The profits earned by the firms are Multiple Choice A1 $20,806 and a2 $9,991. #1 $20.402 and a2= $9.409
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- LuLu Restaurant (LR) and Lucy Café (LC) have an implicit agreement to keep prices high so that both can earn $30,000 profit a year. Below is their complete payoff matrix in terms of thousands of dollars of profit per year and strategic actions a and b. LR’s payoffs are the left and LC’s are on the right. However, in 2014 new owner/managers have taken over both LR and LC and have to decide whether to abide by the implicit agreement or to cheat. LC a b LR a 30, 30 25,32 b 32, 25 26, 26 What strategy will each firm choose and what will be its profit? Is this a Nash equilibrium? Why or why not? Would it be worth it for these new owners/managers to find reach an accommodation and go back to the old implicit agreement? Would this be a Nash equilibrium? Why or why not? Is this game a prisoner’s dilemma? Why or why not?Several firms collude in an oligopoly where the Industry Supply is given by QS = 6 - 5P and Industry Demand is given by, QD = 5P – 5. If the probability that this collusion will continue is given by (1/P*), what is the minimum number of firms required to break the tacit collusion?Olivia is thinking about opening a new bakery (the entrant). There is already a bakery open in her neighborhood (the incumbent), and the owner of the incumbent bakery makes it clear that if Olivia enters the market, they will cut their prices in an attempt to drive the new bakery out of business. Based on the payoff matrix below, is the incumbent’s threat credible? That is, if Olivia opens a new bakery, will the incumbent actually lower their prices? Note: the entrant chooses the row, the incumbent chooses the column High price Low price Enter 1, 2 -1, 1 Don’t enter 0, 10 0, 1 a. Yes, the threat is credible b. No, the threat is not credible
- Price competition between firms, from the firms’ perspective, can be similar to the prisoners’ dilemma. The best outcome for all firms would be for all to charge a high price. However, if the other firms charge a high price, any individual firm has incentives to charge a low price and steal the market. Additionally, if any other firm chooses a low price, each firm should charge a low price too so that it doesn’t get priced out of the market. Explain how price-matching (firms announcing a policy where they match the lowest price a customer can find or will honor a competitor’s coupon) can help firms avoid the Nash equilibrium in which they all charge a low price. Is it misleading for a firm to advertise price-matching as being beneficial to consumers? (Hint: What outcomes of the game are ruled out by the price-matching policy? How does ruling out these outcomes change the game and the decision the firms face?)Price competition between firms, from the firms’ perspective, can be similar to the prisoners’ dilemma. The best outcome for all firms would be for all to charge a high price. However, if the other firms charge a high price, any individual firm has incentives to charge a low price and steal the market. Additionally, if any other firm chooses a low price, each firm should charge a low price too so that it doesn’t get priced out of the market. Explain how price-matching (firms announcing a policy where they match the lowest price a customer can find or will honor a competitor’s coupon) can help firms avoid the Nash equilibrium in which they all charge a low price. Is it misleading for a firm to advertise price-matching as being beneficial to consumers? What outcomes of the game are ruled out by the price-matching policy? How does ruling out these outcomes change the game and the decision the firms face?Pfizer and a competitor, Astra-Zeneca, are considering developing a new drug for a particular illness at the same time. The illness is relatively rare but the fixed cost of production is very high. In particular, the forecast demand for such a drug is insufficient to cover both firms’ costs. Analyse the interaction between the two firms using game theory. Present a payoff matrix to model the situation and analyse it for Nash equilibrium. What can either of these firms do to make their best, most- preferred outcome more likely?
- A total of n ≥ 2 companies are considering entry into a new market. The cost of entry is 30. If only one company enters, then its gross profit is 200. If more than one company enters, then each entrant earns a gross profit of 40. The payoff to a company that enters is its gross profit minus its entry cost, while the payoff to a company that does not enter is 60. Find a symmetric Nash equilibrium in mixed strategies.Consider an oligopolistic industry with N competing firms. Suppose that these firms have no fixed costs and that they all have the same marginal costs. Each firm must choose what quantity to produce independently of each other, and all firms must choose at the same time. If we decrease the number of firms in this industry (to, for example N−1), the market price Group of answer choices A. increases B. decreases C. remains unchanged D. becomes nil E. none of the aboveTwo gas stations, A and B, are locked in a price war. Each player has the option of raising its price (R) or continuing to charge the low price (C). They will choose strategies simultaneously. If both choose C, they will both suffer a loss of $100. If one chooses R and the other chooses C, (i) the one that chooses R loses many of its customers and earns $0, and (ii) the one that chooses C wins many new customers and earns $1000. If they both choose R, the price war ends and they each earn $500. Does player b have a dominant strategy? Explain. What course of action will player A and B choose?
- Three firms produce identical products and compete in a market where the inverse demand function is P(q1, q2, q3) = 78 − q1− q2− q3. Each has a per-unit cost of 14 and zero fixed cost. They simultaneously choose quantities. In scenario (a), find the Nash equilibrium of this game and let A = firm 2's profit in the Nash equilibrium. In scenario (b), assume that the firms form a cartel, i.e., they act as a monopoly and split the profit evenly. If the total quantity produced by the cartel is Q, then the inverse demand is P(Q) = 78 - Q. Let B = firm 2's profit in the cartel. Calculate the value of A - B and enter your answer in the box below. Please round your answer to 3 decimal places (e.g., write 4/3 as 1.333).Two gas stations, A and B, are locked in a price war. Each player has the option of raising its price (R) or continuing to charge the low price (C). They will choose strategies simultaneously. If both choose C, they will both suffer a loss of $100. If one chooses R and the other chooses C, (i) the one that chooses R loses many of its customers and earns $0, and (ii) the one that chooses C wins many new customers and earns $1000. If they both choose R, the price war ends and they each earn $500. Draw the payoff matrix for this game. What is the optimal strategy? Does player A have a dominant strategy? Explain. Does player B have a dominant strategy? Explain How many Nash equilibria does this game have ? what course of action will player A & B choose?Two gas stations, A and B, are locked in a price war. Each player has the option of raising its price (R) or continuing to charge the low price (C). They will choose strategies simultaneously. If both choose C, they will both suffer a loss of $100. If one chooses R and the other chooses C, (i) the one that chooses R loses many of its customers and earns $0, and (ii) the one that chooses C wins many new customers and earns $1000. If they both choose R, the price war ends and they each earn $500. 1. Draw the payoff matrix for this game. B B R C A R (500,500) (0,1000) A C (1,000,0) (-100,-100) 2. What is the optimal strategy? R for A and R for B 3. Does player A have a dominant strategy? Explain. No player A doesn't have a dominant strategy. If player B chooses R, A's best response is to settle on C. If B chooses C, A's best response is to choose C. Since there is no single best response, A does not have a dominant strategy. 4. Does player…