Consider the p-beauty contest game. a group of people wrote down a number between 1 and 100. 2/3rd of the average of all the numbers was calculated. Whoever's answer was closest to the value wins.
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- 8) Three decision makers have assessed utilities for the problem whose payoff table appearsbelow. probabilities and payoffs. S1 S2 S3 D1 500 100 -400 D2 200 150 100 D3 -100 200 300 Probability .2 .6 .2 Indifference Probability for Person Payoff A B C 300 .95 .68 .45200 .94 .64 .32150 .91 .62 .28100 .89…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.* Please be advised this is for practice preperation only ** i just really need help on this - I dont undertsand X is an arbitrary number Suppose the stage game was played for 3 rounds. Consider the following strategy: Round 1: play C. Round 2: play C if both players played C in round 1. Otherwise, play E. Round 3: play D if both players played C in rounds 1 and 2. Otherwise, play E.Ignore discounting (that is, δ = 1). Suppose that both players pick the strategy above. What condition on x is needed to make this strategy profile a SPNE? Hint: remember to check for possible deviations separately for rounds 1 and 2.(a) 5 ≥ x(b) 7 ≥ x(c) 9 ≥ x(d) 11 ≥ x(e) 13 ≥ x
- 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.Which of the following gambles is “unfair”? a. A game that promises to pay you $1 if a coin comes up head and cost you $1 if a coin comes up tail, with no entry fee. b. A game that promises to pay you $10 if a coin comes up head and cost you $1 if a coin comes up tail, with no entry fee. c. A game that promises to pay you $10 if a coin comes up head and cost you $1 if a coin comes up tail, with an entry fee of $4.50 for the right to play. d. All of the above.For the static game, whose payoff matrices are given above, answer the following questions: a. What is the IESDS prediction of the game’s outcome? Explain!b. Find all rationalizable strategies?c. Find all the Nash Equilibrium including mixed strategy equilibrium if any?d. What the difference between the solution concept in (a), (b), and (c).
- Suppose two bidders compete for a single indivisible item (e.g., a used car, a piece of art, etc.). We assume that bidder 1 values the item at $v1, and bidder 2 values the item at $v2. We assume that v1 > v2. In this problem we study a second price auction, which proceeds as follows. Each player i = 1, 2 simultaneously chooses a bid bi ≥ 0. The higher of the two bidders wins, and pays the second highest bid (in this case, the other player’s bid). In case of a tie, suppose the item goes to bidder 1. If a bidder does not win, their payoff is zero; if the bidder wins, their payoff is their value minus the second highest bid. a) Now suppose that player 1 bids b1 = v2 and player 2 bids b2 = v1, i.e., they both bid the value of the other player. (Note that in this case, player 2 is bidding above their value!) Show that this is a pure NE of the second price auction. (Note that in this pure NE the player with the lower value wins, while in the weak dominant strategy equilibrium where both…Question 1 Consider a first-price sealed bid auction of a single object with two biddersj = 1,2 and no reservation price. Bidder 1′s valuation is v1 = 2, and bidder 2′s valuation isv1 = 5. Both v1 and v2 are known to both bidders. Bids must be in whole dollar amounts.In the event of a tie, the object is awarded by a flip of a fair coin.(a) Find an equilibrium of this game.(b) Is the allocation of your answer to (a) efficient?Hedonics setup 1: In class we introduced a case where people have heteroge-neous preferences in our sorting exercise. The types of households, their value of environmental quality, and the number of each type are repeated here for reference. We will ignore school quality in this problem. Neighborhood A will have a price of 0 regardless of the number of people living there, whereas the price equals the number of households in all other neighborhoods. The utility of a person living in a neighborhood is U = aEQ — P. This is the same setup as in class. Card type x Number of HH yellow 6 5 green 5 15 orange 4 10 pink 3 5 blue 2 25 red 1 15 Consider the case below, where all neighborhoods have EQ of 6, except neighbor-hood A which has an EQ of 1. EQ A 1 B 6 C 6 D 6 E 6 F 6 Answers the following Q1. List the equilibrium prices in each neighborhood. Q2. Is this marginal valuation revealed in this equilibrium an overestimate, an under-estimate, or an…
- 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 3.6) For the payoff table below, the decision maker will use P(s1) = .15, P(s2) = .5, and P(s3) =.35. S1 S2 S3 D1 -5000 1000 10,000 D2 -15,000 -2000 40,000 What alternative would be chosen according to expected value?b. For a lottery having a payoff of 40,000 with probability p and -15,000 withprobability (1-p), the decision maker expressed the following indifferenceprobabilities. Payoff Probability10,000 .851000 .60-2000 .53-5000 .50 Let U(40,000) = 10 and U(-15,000) = 0 and find the utility value for each payoff. c. What alternative would be chosen according to expected utility?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?
