if the best response of firm 1: p1 = R1(p2) = (a - p2 - k) / 4 and the best response of firm 2: p2 = R2(p1) = (a - p1 - k) / 4. When subsitituting in a=8 and k=1 how do you solve this step by step to produce a best response functions simultaneously which will = 3.5
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if the best response of firm 1: p1 = R1(p2) = (a - p2 - k) / 4 and the best response of firm 2: p2 = R2(p1) = (a - p1 - k) / 4. When subsitituting in a=8 and k=1 how do you solve this step by step to produce a best response functions simultaneously which will = 3.5
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- 2. Assume a Hawk -Dove game with the following payoff matrix, where the first entry is Animal A's payoff, and the second entry is Animal B's payoff: Animal A Hawk Dove (rows)/Animal B (columns) (-5,-5) (0,10) (10,0) (4,4) Hawk Dove An animal that plays Hawk will always fight until it wins or is badly hurt. An animal that plays Dove makes a bold display but retreats if his opponent starts to fight. If two Dove animals meet they share.Ugly Dolls Inc. (UD) is a firm in Mytown that sells its products on a market under monopolistic competition. The cost function of UD is represented by TC = 100+10Q. Lately, because of the UD is making a big amount of profit, some firms enter the market to compete. If the number of firms entering the dolls market increase, we know that, 1. (a) The price of dolls will drop. (b) The average cost of UD will increase. (c) The quantity sold by UD will drop. (d) All the above answers are correct.Firm 1 and Firm 2 compete in the same product market by setting quantities q₁ and 92, respectively. They have the same marginal cost c₁ = C₂ = 40. The market demand is p=1240 Q, where Q = 91 +92. 19. Suppose the game is played for one period. What are the equilibrium quantities? (a) q₁ = 1000, 92 1000 (b) q₁ = 800, q2 = 800 (c) 91 = 600, q2 = 600 (d) 9₁ = 400, q2 = 400 (e) 9₁ = 200, q2 = 200 In questions 19-21, suppose that this game is repeated for infinitely many periods. Firms have the same discount rate 8. Consider the situation in which the two firms are trying to implement a collusion scheme. With this intent, they employ the following grim-trigger strategy: in the first period, each firm produces the collusion quantity; from period two onwards, the firm keep producing the collusion quantity as long as no firm has ever pro- duced any quantity other than the collusion quantity; otherwise, the firm plays the Nash Equilibrium of the stage game. As you will see, what varies from one…
- Thelma and Louise are competitors in a local beer market and each is trying to decide if it is worthwhile to advertise. If both of them advertise, each will earn a profit of $2000. If neither of them advertises, each will earn a profit of $5000. If one advertises and the other doesn't, then the one who advertises will earn a profit of $7500 and the other will earn a profit of $1000. To make the most money, what should Thelma do and how much profit will she earn? Select one: a. she should advertise, and she will earn $7500 b. she should do whatever Louise does, and will earn either $2000 or $5000 C. she should not advertise, and she will earn $5000 d. she should advertise, and she will earn $2000 Next pageProfits for two competing firms depend on the decisions to advertise or not to advertise as follows: If neither firm advertises, each makes a weekly profit of $100. If one firm advertises while the other does not, the firm that advertises makes $120 while the firm that doesn’t advertise makes $60. If both firms advertise, each firm makes $80. (a) What is the Nash equilibrium? Is this outcome efficient, from the perspective of the two firms? (b) How does the outcome of the game change if the parties can make a binding agreement in advance about advertising practices? (c) How does the game change if it is repeated over the course of many weeks (but the firms cannot make a binding agreement about how much advertising they will do)?Each of 3 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. This implies that if all companies enter the market their payoffs are 10 while if all of them stays out their payoffs are 60. If only one company enters the market its payoff is 170 (while the other two companies’ payoffs are 60). If two companies enter the market their payoffs are 10. Problem Set 2 Due Sunday October 3rd You can discuss the problem set with your classmates, but you are required to submit your independent answers. a) Find all pure strategy Nash equilibria of the game. b) Can you find a mixed strategy Nash equilibrium such that exactly one company plays mixed strategy? If yes, what is it? c) Can you find a mixed…
- A route in the city has trains that depart from station every 20 minutes. It takes a train 40 minutes to make a trip from the station to its destination. For commuters, shorter trips are considered better. Suppose that one such train with 200 commuters on it is about to depart when an additional commuter (who is running slightly late) blocks the doors in order to get on the train, which delays the train by 15 seconds. If this commuter had chosen not to block the train doors, they would have to catch the next train after this one. Question: (Please show the detailed calculation process) What is the private marginal gain of the commuter who barges on the train? What is the marginal spillover effect to all the commuters on the train in terms of travel time? What is the change in the total travel time to all the commuters on the train?If some auction participants for crude-oil field leases have estimates that the oil in the ground is worth $1.2 million, $1.3 million, or $1.5 million with certainty; other auction participants have estimates that the same oil field lease is worth $1.1 million, $1.3 million, or $1.5 million with certainty; and a third group of auction participants have estimates that the same oil field lease is worth $1.1 million, $1.2 million, or $1.3 million, and all three forecasts contain the true common value, what is that value? How would you as auctioneer-seller design an auction to reduce strategic underbidding and realize this true value?Given following normal form i) ii) iii) Player C-1,2 1,-2 1 N 1,-2 -1,2 Player 2 CN Find pure strategy Nash equilibria Find mixed strategy Nash equilibria Draw reaction function for both
- Firm B Q=5 Q=6 Q=5 (24, 24) (30, 10) Q=6 (10, 30) (19, 19) Firm A This table shows a game played between two firms, Firm A and Firm B. In this game each firm must decide how much output (Q) to produce: 5 units or 6 units. The profit for each firm is given in the table as (Profit for Firm A, Profit for Firm B). Refer to Table. The dominant strategy For Firm A is to produce 5 units and the dominant strategy for Firm B is to produce 6 units. 5 units and the dominant strategy for Firm B is to produce 5 units. 6 units and the dominant strategy for Firm B is to produce 5 units. 6 units and the dominant strategy for Firm B is to produce 6 units.In a sideshow game. A player gets 3 balls to place into a Clown's mouth. Each ball is swallowed by the Clown and is then deposited into slots that can hold only 1 ball. Slots are numbered 1 to 9 and prizes are allocated to a player depending on the slot value of the three balls. If for example the first ball landed in slot 8, the second in slot 2 and the third in slot 1, the resulting prize number would be 821 as shown in Figure 3. 3rd 2nd 1st dol 1 2 3 4 5 6 7 8 9 Figure 3: A prize number of 821 is shown for a side show game. a) How many resulting prize numbers are possible in this game? b) How many resulting prize numbers are possible that end with the number 1?Suppose 2 players play the following game infinite times in the future. What should be the minimum value of the time discount so that the equilibrium strategy is (Cooperate, Cooperate)? Player 2 Player 1 Cooperate Defect Cooperate (10, 10) Defect (2, 12) (4,4) (12, 2)