Consider the stage game shown in table below. Suppose this game is played twice. Also, assume that players do not discount future payoffs. That is, 6₁ = √2 = 1. How many SPNEs does the repeated game (where the shown stage game is played twice) have? Player 1 C D L 9,9 11, 6 12, 1 Player 2 6, 11 5,5 1, 1 R 1, 12 1, 1 2,2
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- A researcher studying the effects of a new fertilizer on crop yields plansto carry out an experiment in which different amounts of the fertilizerare applied to 100 different 1-acre parcels of land. There will be fourtreatment levels. Treatment level 1 is no fertilizer, treatment level 2 is50% of the manufacturer’s recommended amount of fertilizer, treatmentlevel 3 is 100%, and treatment level 4 is 150%. The researcher plans toapply treatment level 1 to the first 25 parcels of land, treatment level 2to the second 25 parcels, and so forth. Can you suggest a better way toassign treatment levels? Why is your proposal better than the researcher’smethod?A bunch of cookies should be divided among students by a teacher. Each student writes secretly on a sheet of paper his name and the amount of the cookies (his bid) he wants to get (other students cannot see this number). Then the teacher sorts these bids in ascending order and gives cookies to the students starting from the bid with the smallest amount. If cookies are finished at some point the rest of the students get nothing. If there are several equal bids that cannot be satisfied simultaneously with the current amount of cookies, cookies are equally divided among the students who named these bids. If there are extra cookies, the teacher keeps them. You should assume that cookies are perfectly divisible. Find a Nash Equilibrium in pure strategies. Explain why the set of strategies you propose is indeed a Nash Equilibrium in pure strategies. Explain why there are no other Nash equilibria.When real estate apents sell their own, rather than dients, houses, they leave the houses on the market for a longer time (10 davs longer on average) and wind up with better prices. Suppose that real estate apents earn a commission equal to 3% of the sale value of each house that they help sel. Suppose a real estate apent has an offer on a house of s200,000. The agent can pet a 4% higher offer with more effort and by leaving the house on the market for a few more weeks. If the agent sells the house now, he wil ean a commission of |. By keeping the house on the market and expending more etfort to sel the house, the apert can earn a commission of Thus, the agent paine E for the extra effort and time of keeping the house on the market. Supoose a real estate agent has an offer on a house that he owns. The agent has a current offer of s200,000. but can pt a 4% higher offer with more effort and by leaving the house on the market for a few more weeks, Assume that all of the commission is paid…
- (1) Multi-Party Electoral Competition - In class, we assumed that there are two parties competing in the election. Let us consider the alternative case with three contending parties, A, B and C. Other parts of the game remains the same. In particular, the election is decided by plurality rule, so the party with the largest vote count (share) wins. Moreover, when there is a tie, the tying parties each win with equal probabilities. 1 (a) Consider the action profile where all three parties choose xm = 1/2. Is (1⁄2, ½, ½) a Nash equilibrium? Explain. 2 (b) Now consider the action profile (A, B, C) = (1, 3, 3). Is it a Nash equilibrium? 3' Explain.Pisa Pizza, a seller of frozen pizza, is considering introducting a healthier version of its pizza that will be low in cholesterol and contain no trans fats. The firm expects that sales of new pizza will be $20 million per year. While many of these sales will be to new customers, Pisa Pizza estimaes that 40% will come from customers who switch to the new, healthier pizzai nstead of buying the original version. a) Assume cusotmer will spend the same amount on either version. What level of incremental sales is associated with introducing the new pizza? b) Suppose that 50% of hte cusomters who will switch from Pisa Pizza's orignial pizza to its healthier pizza will switch to another brand if Pisa PIzza does not introduce a healthier pizza. What level of incremental sales is associated with introducing the new pizza in this case?Pag question Player 2 Y1 Y2 Y3 X1 8,5 6,4 11,4 4,8 5,6 Player 1 X2 7,5 12,4 3,3 X3 4,6 For the game given above, ((p1.p2.p3).(q1.q2.q3) is a mixed strategy: The first triplet is Piayer 1's probability allocations to X1, X2, X3. The second triplet is Player 2's probability allocations to Y1, Y2, Y3. Which of the following is true? O a. For Player 2, Y1 is strictly dominated by Y2 Ob. ((p1.p2.p3),(q1.42.q3))- (2/5.2/5,1/5)(3/5.1/5,1/5) is a mixed NE Oc. No action is strictly dominated by any mixed strategy O d. ((pl.p2.p3).(q1.q2.q3)- (1/4.2/4,1/4C/4,0,1/4) is a mixed NE
- Q4: An investor invests $1000 a month, on average, in a stock market security. Because the investor must wait for good "buy" opportunity, the actual time of purchase is random. The investor usu- ally keeps the securities for about 3 years on the average but will sell at random times when a good "sell" opportunity presents itself. Although the investor is generally recognized as a shrewd stock market player, past experience indicates that about 25% of the securities decline at about 20% a year. The remaining 75% appreciate at the rate of about 12% a year. Estimate the inves- tor's (long-run) average equity in the stock market. Hint: use the average number of securities in the market.If Firm 1 chooses to release the console in October with probability of 0.692 or December with a probability of 0.308, then Firm 2 is indifferent between choosing a release date. If Firm 2 released the console in October with probability of 0.50 or December with a probability of 0.50, then Firm 1 is indifferent between choosing a release date Suppose now that instead of choosing the release date at the same time, the firms choose sequentially (but still in advance). Firm A chooses its release date first, then firm B observes that date and chooses its own date. Thepayoffs are otherwise the same as above. Represent the game tree corresponding to this dynamic game.Asap
- DN4 Suppose that two investments have the same three payoffs, but the probability associated with each payoff differs, as illustrated in the table below: Probability (Investment B) Payoff $300 $250 $200 Probability (Investment A) 0.10 0.80 0.10 0.30 0.40 0.30 Nahoko has the utility function U= 51, where I denotes the payoff. Which investment should she choose?n people guess an integer between 1 and 100, and the winner is the player whose guess is closest to the mean of the guesses + 1 (ties broken randomly). Which of the following is an equilibrium: a) All announce 1. b) All announce 50. c) All announce 75. d) All announce 100Each of Player 1 and Player 2 chooses an integer from the set {1, 2, ..., K}. If they choose the same integer, P1 gets +1 and P2 gets -1; if they choose different integers, P1 gets -1 and P2 gets +1. (a) Show that it is a NE for each player to choose every integer in {1, 2, ..., K} with equal probability, K1 . (b) Show that there are no NE besides the one you found in (a).