Two companies have to choose their prices at the same time, at either high (pH) or low (pL) levels. If both choose high (pH), they will share the monopoly profits of 50 thousand euros. Otherwise, 40 thousand euros will be distributed. If Company 1 chooses high (pH) and Company 2 low (pL), then it will receive zero profits and its opponent will have profits equal to 35 thousand euros. The opposite will happen if firm 1 chooses low (pL) and the other firm high (pH). The Nash balance of the game is formed in the pair of strategies а) рH, рH b) pH, pL c) pL, pL d) pL, pH
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- 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?Consider the two-round bargaining game. The minimum the seller will sell his home for 188,000 and the maximum the buyer is willing to pay is $200,000. Both players know these two amounts and are bargaining over the difference (M=$1200). Assume the disagreement values are zero for both players. Player 1 moves first by making a proposal and Player 2 can accept and reject. If player 2 rejects Player’s 1 proposal, then Player 2 gets to make a proposal, which Player 1 can reject and accept. The game is then over. Suppose the both players discount the future income at the rate d=0.2 per period. That is, $0.20 now is equivalent to $1,00 received next round. Find the equilibrium for this 2-round game. a) Draw the game tree b) What is the sale price of home? c)Which player gets the larger share of M?There are two firms in the market (duopoly). These two firms are competingsimultaneously. The first firm chooses its output level (x) by predicting the second firm’soutput (y). Let c denote the total cost function c(x) = x and c(y) = y. Also, let’s assumethat the inverse demand function is p(Y) = 7 - Y where Y = x + y. (1) Obtain the reactionfunction of the first firm. (2) Find the equilibrium (output and profit of each firm) whentwo firms simultaneously compete
- Suppose three Cournot competitors, each with costs Ci = 30qi, face an inverse market demand curve of P = 480 – 4Q. Suppose merging will not change costs. a. Find profits for the three firms. Note: Don’t round your answers. How will the profits change for F1 and for F2|3 if F2 and F3 merge? b. Suppose that after the merger occurs, F1 and the new firm F2|3 successfully collude at setting the monopoly price and output, and splitting the resulting monopoly profits. How, if at all, does this change the impact of the merger on F1 and on the merged firm?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 :))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. )
- Consider a quantity-setting duopoly. The two firms are Alpha, Ltd. and Beta, Inc. The demand schedulein this market is: p Qd180 150155 175130 200Each firm has a constant marginal cost of 30 per unit. Suppose each firm can choose to produce either 75units or 100 units. Firms make their quantity choices simultaneously and the market price is whatever itneeds to be to sell the total output in the market.(a) Draw up the normal form game matrix, showing the players, strategies, and payoffs. Show your workdetermining the profits in each box in the matrix.(b) Determine the Nash equilibrium of this game.(c) Suppose the firms were able to come to an agreement to make more profit. What would this agreementbe?(d) Explain how the government might respond to such an agreement and why.Consider a quantity-setting duopoly. The two firms are Alpha, Ltd. and Beta, Inc. The demand schedulein this market is:p Qd180 150155 175130 200Each firm has a constant marginal cost of 30 per unit. Suppose each firm can choose to produce either 75units or 100 units. Firms make their quantity choices simultaneously and the market price is whatever itneeds to be to sell the total output in the market.(a) Draw up the normal form game matrix, showing the players, strategies, and payoffs. Show your workdetermining the profits in each box in the matrix.(b) Determine the Nash equilibrium of this game.(c) Suppose the firms were able to come to an agreement to make more profit. What would this agreementbe?(d) Explain how the government might respond to such an agreement and whyIsabella runs an IT solutions business for her college peers and has only one competitor, Franco.Isabella and Franco have decided to collude andprovide monopoly-level output. Given that theyare both freshmen and intend to run their businesses for the next three years, is this agreementsustainable? Would your answer change if Francoknew he planned to transfer to another collegenext year?
- Suppose two Bertrand competitors, F1 and F2, make identical products for a market with inverse demand P = 600 – 0.5Q. Both firms have the same costs Ci = 20qi, and each firm has sufficient capacity to supply the entire market. a. What prices will the firms choose? How much might each produce and what profit would they make? Is the result a Nash equilibrium? Explain. b. Suppose F1 improves its efficiency, reducing its cost to C1 = 16q1. What will happen in this market? Explain. c. Assume now that the firms have their original identical costs, but that F1 has only 100 units of capacity and F2 has only 200 units of capacity. What prices will the firms choose now? Explain why neither firm will want to decrease its price at the equilibrium you identify. Why would neither firm want to increase its price? Prove this for F1.Consider the strategic voting game discussed at the endof this chapter, where we saw that the strategy profile (Bustamante, Schwarzenegger,Schwarzenegger) is a Nash equilibrium of the game. Show that (Bustamante, Schwarzeneg-ger, Schwarzenegger) is, in fact , the only rationalizable strategy profile. Do this by firstconsidering the dominated strategies of player L. (Basically, the question is asking youto find the outcome of the iterative elimination of strictly dominated strategies)Consider a “punishment” variation of the two-firm oligopoly situation shown in Figure 14.1. Suppose that if one firm sets a low price while the other sets a high price, then the firm setting the high price can fine the firm setting the low price. Suppose that whenever a fine is imposed, X dollars is taken from the low-price firm and given to the high-price firm. What is the smallest amount that the fine X can be such that both firms will want to always set the high price?