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List five types of infinitely repeated games
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- If you were playing a game of Stag Hunt, would you rather play the simultaneous version of the game or the sequential version? Why?Micro Nash game theory Show that if in a game G, the sets of actions (A i) i in N are compact, and the payment functions (u i) i in N are continuous, then for all i in N, the application of Best response has a closed graph. Conclude that the application of best response has a closed graph.Game theory- please help.
- Use a decision tree to solve a sequential gameProblems associated towards unique outcomes in games where multiple Nash equilibria exist”The bimatrix represents a simultaneous move game between Rowena and Colin. Rowena's payoff is the left number in each cell. ROWENA Up Down 0.25Left +0.75Right 0.65Left +0.35Right Find Colin's mixed strategy that makes Rowena indifferent between a pure strategy of playing Up and a pure strategy of playing Down. 0.5Left +0.5Right Left 1,16 2,20 0.45Left +0.55Right COLIN Right 4,6 3,40
- Consider the following sequential game: D 1 (0,0) R D 2 (-1,2) R d (1,1) how to write this game in normal form r d 2 (0, 3) r (2, 2)Please no written by hand solutions Consider a game between two friends, Amy and Brenda. Amy wants Brenda to give her a ride to the mall. Brenda has no interest in going to the mall unless her favorite shoes are on sale at the large department store there. Amy likes these shoes as well, but she wants to go to the mall even if the shoes are not on sale. Only Amy subscribes to the newspaper, which carries a daily advertisement of the department store. The advertisement lists all items that are on sale, so Amy learns whether or not the shoes are on sale by showing the newspaper to Brenda. But this is costly for Amy, because she will have to take the newspaper away from her sister, who will yell at her later for doing so. In this game, nature first decides whether or not the shoes are on sale, and this information is made known to Amy (Amy observes whether nature chose S or N). Nature chooses S with probability p and N with probability 1-p. Then Amy decides whether or not to take the…Profits 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)?
- 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?Question: Determine the set of rationalizable strategies for each of the following games. Player 2 Player 2 (0, 4) (3, 3) (4, 0) Player 2 (2,0) (3, 4) (1,3) (4, 2) (2, 3) (4,0) (3, 3) (0, 4) (1,1) Player 1 Player 1 (1,2) (0,2) | (3,0) Player 2 D D (5, 1) | (0, 2) | Player 1 (4, 6) (3, 5) (6, 3) (0, 1) (2,1) Player 2 (8, 6) (1,0) (0,8) (8, 2) (0, 1) (2, 6) (5, 1) (4, 4) (1,0) Player 1 (6,0) (2,8) D D Player 2 (8, 10) (6, 4) (2, 2) (0,0) (0,0) (3,3) (4, 1) (8, 5) Player 1 Player 1 B B Player 2 Player 2 (8, 10) (6, 4) (3, 10) (6, 4) (4, 1) (8, 5) (4, 1) (8, 5) Player 1 A Player 1 B BDerive all of the rationalizable strategies for the game shown.