5. Three companies are considering entering into a new market. The cost of entry is 30. If only one company enters, then its revenue is 150. If more than one company enters, each gets a revenue of 50. The payoff to each entrant is its revenue minus the cost of entry, while the payoff to a company that does not enter is 60. The entry decision is made simultaneously. What is the symmetric NE in mixed strategies?

5. Three companies are considering entering into a new market. The cost of entry is 30. If only one company enters, then its revenue is 150. If more than one company enters, each gets a revenue of 50. The payoff to each entrant is its revenue minus the cost of entry, while the payoff to a company that does not enter is 60. The entry decision is made simultaneously. What is the symmetric NE in mixed strategies?

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter15A: Auction Design And Information Economics

Section: Chapter Questions

Problem 10E

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a) Write out the extensive form of a game between a farmer (playing in the first round) and nature (playing a mixed strategy in the second round). Assume that the farmer can either pay a cash rent of $1500 for land (English system) or 1/2 of crop production to the landlord (sharecropping). Assume the farmer is planting corn and will produce 2 tons of corn. Assume that nature has a 50% chance of playing a strategy in which the price of corn is $3500/ton and a 50% chance of playing a strategy in which the price of corn is $500/ton. The farmer keeps any money left after paying cash rent and sells any corn left after paying the landlord in sharecropping. b)What is the most that a risk neutral farmer would be willing to pay for an accurate prediction of the price of corn in problem 1 before choosing whether to pay cash rent or sharecrop?
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.
16. Boeing is considering whether it should develop its next aircraft with a wide body (WIDE) or whether it should make it a long aeroplane (LONG). Airbus, Boeing's competitor, also has a choice between choosing WIDE or LONG. The payoffs to the two companies are shown in the payoff matrix below. What are the (pure strategy) Nash equilibrium in this game? (The first action in the brackets is the strategy of Boeing, while the second is Airbus's strategy.) Airbus WIDE LONG WIDE 40 for Airbus Boeing 50 for Boeing O for Airbus 0 for Boeing LONG 0 for Airbus 0 for Boeing 50 for Airbus 40 for Boeing a. (WIDE, WIDE) for Boeing and Airbus respectively) and (WIDE, LONG) b. (LONG, WIDE) and (WIDE, LONG) c. (WIDE, WIDE) d. (LONG, LONG) e. (WIDE, WIDE) and (LONG, LONG)
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…
Two firms, X and Y, are planning to market their new products. Each firm can develop TV, Laptop. Market research indicates that the resulting profits to each firm for the alternative strategies are given by the following payoff matrix : MATRIX IS ATTACHED Find the Nash equilibria for this game, assuming that both firms make their decisions at the same time. (explain the decision step by step) If each firm is risk averse and uses a maximin strategy, what will be the resulting equilibrium? (explain the decision step by step) What will be the equilibrium if Firm X makes its selection first? If Firm Y goes first?
4. You have probably had the experience of trying to avoid encountering someone, whom we will call Rocky. In this instance, Rocky is trying to find you. It is Saturday night and you are choosing which of two possible parties to attend. You like Party 1 better and, if Rocky goes to the other party, you get a payoff 20 at Party 1. If Rocky attends Party 1, however, you are going to be uncomfortable and get a payoff of 5. Similarly, Party 2 gives you a payoff of 15, unless Rocky attends, in which case the payoff is 0. Rocky likes Party 2 better, but he is likes you. He values Party 2 at 10, Party 1 at 5, and your presence at either party that he attends is worth an additional payoff of 10. You and Rocky both know each others strategy space (which party to attend) and payoffs functions.
1.a) If the three executives of a fraudulent organization report nothing to the authorities, each gets a payoff of 100. If at least one of them blows the whistle, then those who reported the fraud get 28, while those who didn’t get -100. Suppose they play a symmetric mixed-strategy Nash equilibrium where each is silent (does not report fraud) with probability p. What is p?A, 0.1B, 0.28C, 0.5D, 0.8 b) In a two-player game, with strategies and (some known and some unknown) payoffs as shown below, suppose a mixed-strategy equilibrium exists where 1 plays C with probability 3/4, and Player 2 randomizes over X, Y, and Z with equal probabilities. What are the pure-strategy equilibria of this game? A, (A, Y) and (B, X)B, (A, Z) and (C, Y)C, (B, X) and (C, X)D, (C, X) and (C, Y)
Problem 6. Does there exist a two-player game that has a pure NE but best response dynamics may not converge? If the answer is yes, construct such a game. Otherwise, explain why this is not possible.
There are three players in this simultaneous move game. Player-3 chooses between game A and game B. Player-1 chooses between U, M and D. Player-2 chooses between L and R. The payoffs are given below: P-1 U M D A P-2 L R 5,5,0 1,4,0 6,4,5 2,5,3 3,1,2 3,3,1 Find all pure strategy N.E. of this game. P-1 U M D L 4,8,0 4,1,3 3,5,1 B P-2 R 2,1,0 3,3,3 0,3,0
Is there a Nash Equilibrium for this game? If so, what is it? O The Nash Equilibrium is for both first to choose the high price. O The Nash Equilibrium is for both first to choose the low price. O The Nash Equilibrium is for Chevron to choose the high price while Shell chooses the low price. O The Nash Equilibrium is for Shell to choose the high price while Chevron chooses the low price. O There is no Nash Equilibrium for this game.
Write out the extensive form of a game between a farmer (playing in the first round) and nature (playing a mixed strategy in the second round). Assume that the farmer can either pay a cash rent of $1500 for land (English system) or 1/2 of crop production to the landlord (sharecropping). Assume the farmer is planting corn and will produce 2 tons of corn. Assume that nature has a 50% chance of playing a strategy in which the price of corn is $3500/ton and a 50% chance of playing a strategy in which the price of corn is $500/ton. The farmer keeps any money left after paying cash rent and sells any corn left after paying the landlord in sharecropping. What is the most that a risk neutral farmer would be willing to pay for an accurate prediction of the price of corn in problem 1 before choosing whether to pay cash rent or sharecrop?
a. b. Each firm has four alternative strategies, and a certain profit/payoff is associated with each strategy. The numbers in the payoff matrix denote firm A's profit (in thousands of dollars). The total amount of profit that can be earned by the two firms together is $20000. (This is called a "constant sum game.") Firm B's profit is therefore $20000 minus firm A's profit. What strategies will the two firms select? Is the game strictly determined? If so, how much does each firm gain? B's strategies A's strategies ↓ Increase Advertising Decrease Price Increase Price Alter Product Increase Advertising 0 11 8 11 Decrease Price 8 10 6 2 Increase Price 7 12 15 Alter Product 4 15 3 12 Suppose now that due to a change in consumer preferences, firm A's "Increase Price" strategy pays off better than before when firm B elects to "Decrease Price," that is, the payoff rises from 6 to 14. What strategies will the two firms now select? Is the game strictly determined? If so, how much does each firm…