1 2 W X y a 0,1 1,2 2,4 b 1,4 2,3 0,1 с 7,5 6,2 5,3 Is player 1's strategy x dominated? If yes, provide a strategy that dominates x. If no, provide a belief that makes x a best response.
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CS 15
Subject - Economics
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- Choose the correct answer. A strategy AA is "dominant" for a player X if: A. Every outcome under strategy AA generates positive payoffs. B. Irrespective of any of the possible strategies chosen by the other players, strategy AA generates a higher payoff than any other strategy available to player X. C. Strategy AA is the best response to every strategy of the other player. D. Strategy AA contains among its outcomes the highest possible payoff in the game. E. Strategy AA is the best response to the best strategy of the other player.onsider the game described by the ff table. what is thE best response for the column player if he/she knows that the row player will make the Y move?1\2 X Y Z A 8,6 12,5 5,2 B 4,8 8,10 10,12 Suppose Player 2 believes Player 1 will pay a mixed strategy θ1 (A,B) = (θ, 1- θ). Find a range of the frequency of play of A (i.e., values of θ) that makes the pure strategy Y a best response. The minimum value of θ = _____ The maximum value of θ = _____
- Find all NE of the stage game.(b) Consider a two-period game without discounting in which the stage game is played ineach period. Find all pure strategy SPNE.(c) What’s the min-max payoff of each player?(c1) Consider pure strategies only.(c2) Consider all strategies, including the mixed ones.(d) Now suppose the stage game is repeated infinitely many times. Use the Fudenberg-Maskin Folk theorem to find all possible values of payoff that can be supported as aSPNE.Mohamed and Kate each pick an integer number between 1 and 3 (inclusive). They make their choices sequentially.Mohamed is the first player and Kate the second player. If they pick the same number each receives a payoff equal to the number they named. If they pick a different number, they get nothing. What is the SPE of the game? a. Mohamed chooses 3 and Kate is indifferent between 1, 2 and 3. b. Mohamed chooses 3 and Kate chooses 1 if Mohamed chooses 1, 2 if Mohamed chooses 2, and 3 if Mohamed chooses 3. c. Mohamed chooses 1 and Kate chooses 1 if Mohamed chooses 1, 2 if Mohamed chooses 2 and 3 if Mohamed chooses 3. d. Mohamed chooses 3 and Kate chooses 3.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.)
- What is the secure strategy for player B in the game presented in TablePortsmouth Bank has foreclosed on a home mortgage and is selling the house at auction. There are three bidders for the house, Emily, Anna, and Olga. Portsmouth Bank does not know the willingness to pay of these three bidders for the house, but on the basis of its previous experience, the bank believes that each of these bidders has a probability of 1/3 of valuing it at $600,000, a probability of 1/3 of valuing at $500,000, and a probability of 1/3 of valuing it at $200,000. Portsmouth Bank believes that these probabilities are independent among buyers. If Portsmouth Bank sells the house by means of a second- bidder, sealed- bid auction (Vicktey auction), what will be the bank's expected revenue from the sale?Consider the game of Chicken in which each player has the option to “get out of the way” and “hang tough” with payoffs: Get out of the way Hang tough Get out of the way 2,2 1,3 Hang tough 3,1 00 a. Find all pure strategy Nash equilibria, if they exist b. Let k be the probability that player 1 chooses “hang tough” and u be the probability that player two chooses “hang tough.” Find the mixed stragety Nash equilibria, if they exist
