he outcome is a Nash-Coumot equilibrium, why di rose less than the firma' costs in this oligopoly because A demand is not perfectly inelastic. . consumers are not price sensitive. . the firms are price takers. air travel has no close substitutes.
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- Sometimes oligopolies in the same industry are very different in size. Suppose we have a duopoly where one firm (Film A) is large and the other film (Film B) is small, as the prisoners dilemma box in Table 10.4 shows. Assuming that both films know the payoffs, what is the likely outcome in this case?Discuss what can be the expected resultof the firms in the Cournot oligopoly, that is, that can be the expected Nash Equilibrium solution fora household cleaning appliance firm.1. Prove that every trembling-hand perfect equilibrium (for the agent normal form) is sequential. Show by example that the converse is false. The remaining problems in this chapter concern game-theoretic variations on the classic models of oligopoly. They are primarily about those models and so relate more to material in other chapters, but they could not have been posed until we had covered Nash equilibria and sub game perfection. 2. Prove that in the Bertrand game, if prices must be charged in integer multiples of a penny, then there is always at least one Nash equilibrium in which players do not use weakly dominated strategies.
- Imagine that firm X chooses their quantity first, then firm Y observes the quantity of firm X and chooses their own quantity. What is the subgame perfect Nash Equilibrium? Is there a first or second-mover advantage here? You don't need to draw the whole game tree but you should give some kind of explanation for how you came to this equilibrium. (You may assume that firm X can only choose quantities that are multiples of 200. This prevents you from having to deal with prices that are not on the schedule and makes firm Y's strategy easier to write. )Two oligopolistic firms have to decide on the pricing strategy. Each can either choose either a high or a low price. If they both choose a high price, each will make $12 million, but if they both choose a low price, each will make $ 8 million. If one sets a high price and other a low one, the low-priced firm will make $16 million, but the high-priced firm will make only $4 million. It is illegal for each firm to communicate with each other. a) Which strategy would both of them ultimately opt for? b) What would be the pay-off for this strategy?What is the distinguishing characteristics of oligopoly in relation to the other forms of the other market organizations? What is its significance? In which sector of the USA economy is oligopoly most relevant?An oligopolistic firm from the telecommunication industry in USA follows demand-and-cost situation in 2009.Price in USD($) Quantity Total cost20 7 3619 8 4518 9 5417 10 6316 11 7215 12 81i. How much output should the oligopolistic produce? What price should it charge and what is the maximum profit can this firm earns?
- The French economist Antoine Cournot developed an interesting model of competition in an oligopoly that now bears his name. In a Cournot oligopoly, all of the firms know that the total output from all firms will determine the price (based on the downward-sloping market demand curve), but they make independent and simultaneous decisions about how much output to produce. Cournot developed this model after observing how a spring water duopoly (two firms) behaved. So let’s look at a duopoly example.For each firm to decide how much to produce, it must make a guess about how much the other firm is going to produce. Also, the firms basically assume that once the other firm has decided how much to produce, it can’t really change its decision.Here’s an example. Suppose the market demand curve for gallons of fresh spring water looks like the one below and, to keep things simple, the marginal cost of spring water is zero. If Firm X believes that Firm Y is going to produce 100 gallons of spring…Two firms produce identical products at zero cost, and theycompete by setting prices. If each firm charges a low price,then both firms earn profits of zero. If each firm charges ahigh price, then each firm earns profits of £30. If one firmcharges a high price and the other firm charges a low price,the firm that charges the lower price earns profits of £50, andthe firm charging the higher price earns profits of zero. (a) Which oligopoly model best describes this situation?(b) Write this game in normal form.(c) Suppose the game is infinitely repeated. Can theplayers sustain the "collusive outcome" as a Nashequilibrium if the interest rate is 50 percent? Explain. Please answer the a, b and c parts.Consider a situation where two firms, 1 and 2, compete by choosing prices simultaneously. Theycan either compete (charge a low price) or cooperate (collude, charging a high price). The firmsplay this competition game repeatedly and indefinitely, using a grim trigger strategy toincentivize cooperation. They use the same interest rate, i, to discount future payoffs. Payoffsare $4,050 when both firms cooperate and $3,600 when they compete. If one firm charge a lowprice while the other charges a high price, the firm charging the low price gets $7,200, and theother gets zero, but now assume there is a 10% chance that aregulatory agency will give both firms a $1,500 fine in each period if they are caught colluding.Find the condition on the interest rate, i , necessary for sustaining the cooperative equilibrium.Which of the following statements is correct?(a) For any i < 1/7 the firms will cooperate.(b) For any i < 1/11 the firms will cooperate.(c) For any i > 1/11 the firms will…
- Two firms with differentiated products are competing in price. Firm A and B face thefollowing demand curves: Q_A = 70 − 2P_A + P_B and Q_B = 120 − 2P_B + P_Arespectively. Assume production is costless.a. Give equations for and graph each firm’s reaction curve.b. If both firms set their prices at the same time, what is the Nash equilibriumprice, quantity, and profit for each firm?c. Suppose A sets its price first and then B responds. What price and quantitydoes each firm set now? Is it advantageous to move first?d. Compare the profits from part b and c. Which firm benefits more from thesequential price choosing? (Please do b-d, thanks :))Untied and Air ’R’ Us are the only two airlines operating flights between Collegeville and Bigtown. Each airline can charge either a high price or a low price for a ticket. The accompanying matrix shows their payoffs, in profits per seat (in dollars), for any choice that the two airlines can make. Suppose the two airlines play a one-shot game—that is, they interact only once and never again. What will be the Nash (noncooperative) equilibrium in this one-shot game? Explain why this is the likely outcome. Now suppose the two airlines play this game twice. Each airline then considers the future and decides on a “tit-for-tat” strategy, that is, it starts off charging the high price in the first period, and then in the second period it does whatever the other airline did in the previous period. If both play this…Suppose that there are two firms in a market, firm 1 and firm 2. The marketis declining in size. The game starts in period 0, and the firms can compete in periods 0, 1,2, 3, ... (i.e., indefinitely) if they so choose. Duopoly profits in period t for firm 1 are equalto 105 −10t, and they are 10.5 −t for firm 2. Monopoly profits (those if a firm is the onlyone left in the market) are 510 −25t for firm 1 and 51 −2t for firm 2. At the start of eachperiod, each firm must decide either to “stay in” or “exit” if it is still active (they do sosimultaneously if both are still active). Once a firm exits, it is out of the market forever andearns zero in each period thereafter. Firms maximize their (undiscounted) sum of profits.What is this game’s subgame perfect Nash equilibrium?