A total of 10 players are each choosing a number from {0,1,2,3,4,5,6,7,8}. If a player's number equals exactly half of the average of the numbers submitted by the other nine players, then she is paid $100; otherwise, she is paid 0. Solve for the strategies that survive the IDSDS.
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A total of 10 players are each choosing a number from {0,1,2,3,4,5,6,7,8}. If a player's number equals exactly half of the average of the numbers submitted by the other nine players, then she is paid $100; otherwise, she is paid 0. Solve for the strategies that survive the IDSDS.
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- 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…15. A total of 10 players are each choosing a number from {0,1,2,3,4,5,6,7,8). If a player's number equals exactly half of the average of the numbers sub- mitted by the other nine players, then she is paid $100; otherwise, she is paid 0. Solve for the strategies that survive the IDSDS.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?
- AsapThree players (player 1, player 2 and player 3) each chooses a positive integer QE {1, 2, 3, . 100}. If all three players choose the same integer Q, each player gets $100/3. If all three players choose different integers, the player with the largest integer gets $100, and the two other players get $0. If two players choose the same integer Q, and the third player chooses a different integer Q', then the player playing Q' gets $0, and the two players who played Q get $50 each. Find 2 Nash equilibriums in this game. ....if w = 6 (b) To which strategy t2 is the strategy t1 = 4 a best response? (If your answer is a fraction, report it in lowest terms.)
- Firm B Q=5 Q=6 Q=5 (24, 24) (30, 10) Q=6 (10, 30) (19, 19) Firm A This table shows a game played between two firms, Firm A and Firm B. In this game each firm must decide how much output (Q) to produce: 5 units or 6 units. The profit for each firm is given in the table as (Profit for Firm A, Profit for Firm B). Refer to Table. The dominant strategy For Firm A is to produce 5 units and the dominant strategy for Firm B is to produce 6 units. 5 units and the dominant strategy for Firm B is to produce 5 units. 6 units and the dominant strategy for Firm B is to produce 5 units. 6 units and the dominant strategy for Firm B is to produce 6 units.The decision tree below describes the game faced by firm H and firm T. The payoffs are profits in million of US$. The SPNE is(are): (Build large, Build large) (Build Small, Build Small) (Build Small, Build Large) (No build, Build Large) (Build Large, No Build)Which one is the best strategy for Player 1? Player 1 (10, 20) Leave Leave Cooperate Stay Cooperate Player2 Not cooperate Stay (15, 14) Not cooperate Leave Player 2 (17, 11) Stay (16, 12)
- Consider the following representation of a Normal form game. actions w a (45,22) (10,38) (42,13) (10,7) (p,28) (15,40) (q,10) (44,10) (20,22) (14,31) (27,13) (12,8) d. (20,41) (9,48) (28,24) (18,32) Here each cell in the table represents an ordered pair. First element is payoff of the first player and second element is payoff of the second player. The letters a, b, c, d, x, y, z, w represent the actions. Write down the table in your answer script too. Now answer the following questions: 1. What is the distinction between strictly dominant strategy and weakly dominant strategy? Is it reasonable for a player to play a strictly dominated strategy? Explain why. 2. What are the minimum values for p and q that will make ba strategy that strictly dominates all other strategies for player 1, assuming both p and q are natural numbers? 3. Does player 2 have any strictly dominated pure strategy? If yes, which pure strategy dominates that strategy? If the submit button is off it is beacuse the due…AirTrain and BigJet are considering starting a nonstop service from Pittsburgh to Las Vegas. Assume that no other airlines serve this route. Market demand is such that if there is one airline serving the Pittsburgh to Las Vegas route the profit will be $20000. If two airlines serve the route, each will lose $5000. If an airline chooses not to enter this market, their profit is $0. Illustrate the game in normal (matrix) form, if the decision must be made simultaneously. Find the pure strategy Nash equilibriaThree married couples in the state of Maryland—Bob and Carol, Ted and Alice, and Ross and Mike (remember, same-sex marriage is legal in the state of Maryland)—are thinking about renting a boat to go sailing on the Chesapeake Bay. The cost of a boat rental is $600. Each of the three couples puts some amount of money in an envelope. Thus, each player in this game is a couple. If the total amount collected is at least $600, then the boat is rented. If the amount collected is more than $600, then the money left over after renting the boat is spent on wine. If the total amount collected is less than $600, then they do not rent the boat, and the money is spent on a dinner. Assume the benefit to a couple from the boat trip is 400, the benefit from each dollar spent on wine is 50 cents, the benefit from each dollar spent on dinner is 40 cents, and the personal cost of the contribution to a couple equals the amount of contribution. For example, if the boat is rented, $50 of wine is purchased…