1) Is there a separating equilibrium in the game above? If so, what are the equilibrium strategies of the candidate and the admission officer, and what are the beliefs of the admission officer? What constraints need to be satisfied?
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- Halsen, a marketing manager at Business X, has determined four possible strategies (X1, X2, X3, and X4) for promoting the Product X in London. She also knows that major competitor Product Y has 4 competitive actions (Y1, Y2, Y3 and Y4) it’s using to promote its product in London, too. Ms. Halsen has no previous knowledge that would allow her to determine probabilities of success of any of the four strategies. She formulates the matrix below to show the various Business X strategies and the resulting profit, depending on the competitive action used by Business Y. Determine which strategy Ms. Halsen should select using. Maximax, maximin or minimax regret? Business X Strategy Business Y Strategy Y1 Y2 Y3 Y4 X1 25 57 21 26 X2 17 29 20 34 X3 47 31 32 37 X4 35 27 30 35Halsen, a marketing manager at Business X, has determined four possible strategies (X1, X2, X3, and X4) for promoting the Product X in London. She also knows that major competitor Product Y has 4 competitive actions (Y1, Y2, Y3 and Y4) it’s using to promote its product in London, too. Ms. Halsen has no previous knowledge that would allow her to determine probabilities of success of any of the four strategies. She formulates the matrix below to show the various Business X strategies and the resulting profit, depending on the competitive action used by Business Y. Determine which strategy Ms. Halsen should select using, the following decision criteria. Please explain your answer for each strategy. a)Maximax; b)Maximin; c)Minimax regret Business X Strategy Business Y Strategy Y1 Y2 Y3 Y4 X1 25 57 21 26 X2 17 29 20 34 X3 47 31 32 37 X4 35 27 30 35A mobile provider has two types of deals. Currently the provider has 1 million customers, 65% of those have deal 2, and the rest have deal 1. A customer with deal 1, after in average 5 months, may either change the type of the deal (60% of cases) or leave the provider at all (the rest of cases). A customer with deal 2 may also leave the provider; it happens in average after 8 months of using deal 2. It is forbidden do change deal 2 to deal 1. Customers can make their decisions at any time. We assume also that those who left the provider do not return back. (i) Sketch the transition diagram and write down the generator matrix. (Keep time in months. Note that the state space here contains three states.)How many of the current customers are expected to have deals of type 2 in 6 months? (Round the answer to the nearest integer.)
- 1.4. Suppose you are against one of two alternatives but 90% of theelectorate disagrees with your position and favors that option. Is there avoting method that is anonymous, neutral, and monotone that preventsthat option from being selected as the winning alternative?Consider two firms who are engaged in a Research and Development (R&D) "con- test". Both firms simultaneously expend resources to try to win the contest (which may mean developing a superior product or developing a product before the com- petitor). If the two firms expend bị and b2, respectively, on R&D, the probability that firm 1 wins the contest is if b1 = b2 =0 BE otherwise P1(b1, b2) = where r is some exogenous constant, r E (0, 0). If firm 1 wins the contest, it will subsequently earn revenue of 1 (not including the cost of R&D, b1). If firm 1 loses the contest, it will earn zero revenue, and thus lose bj in total. Hence, firm l's expected profit is n'(b1,b2) = p1(b1,b2) - b1. Everything is symmetric for firm 2. i. How does p1(b1,0) depend on b1? Is it an equilibrium for both firms to spend nothing on R&D (b1 = b2 = 0)? Prove and explain your answer. For which values of r is n' (b,b2) concave in b1 when b2 > 0? ii. Consider the possibility of a symmetric pure-strategy…A seller will run a second-price, sealed-bid auction for an object. There are two bidders, a and b, who have independent, private values v; which are either 0 or 1. For both bidders the probabilities of v; = 0 and v; = 1 are each 1/2. Both bidders understand the auction, but bidder b sometimes makes a mistake about his value for the object. %3| Half of the time his value is 1 and he is aware that it is 1; the other half of the time his value is 0 but occasionally he mistakenly believes that his value is 1. Let's suppose that when b's value is 0 he acts as if it is 1 with probability 1/2 and as if it is zero with 2 probability. So in effect bidder b sees value 0 with probability 1/4 and value 1 with probability 4. Bidder a never makes mistakes about his value for the object, but he is aware of the mistakes that bidder b makes. Both bidders bid optimally given their perceptions of the value of the object. Assume that if there is a tie at a bid of x for the highest bid the winner is…
- An author is trying to choose between two publishing companies that are competing for the marketing rights to her new novel. Company A has offered the author $10,000 plus $2 per book sold. Company B has offered the author $2,000 plus $4 per book sold. The author believes that four levels of demand for the book are possible are: 1,000, 2,000, 3000 and 5000 books are sold. If the probabilities of each level of demand are as follows: Demand Probability 1000 0.31 2000 0.32 3000 0.25 5000 0.12 Construct the payoff table for each level of demand for company X and company Y. What are the expected monetary value (EMV) and expected opportunity loss (EOL)? Hence determine the best decision that this author should do.Initially there is a dollar on the table and player-1 can either pick it up or say “Pass". If he picks the money up, the game ends. If he passes, another bill is added, and player-2 has the same options. If there are 4 passes the game ends and the four bills are removed from the table. Player-1 is paid 3.5 and player-2 is paid 3.5. the sub-game perfect equilibria are (a) (1, 0) (b) (0,2) (c) (3, 0) (d) (0, 4)Each of the two players independently (and simultaneously with the other) decides whether to go to a play or a concert. Each would rather go with the other to a concert than with them to a play, but prefers this to not being together, in which case they don't care where they go alone. Additionally, each is indifferent between attending the play together and participating in a lottery where both go to the concert with a probability of ¾ and to different events with a probability of ¼. Describe the game in matrix form and find all its equilibria under the assumption that the players have von Neumann-Morgenstern preferences.
- Wayne Enterprises had several salespersons that worked for a contract salary. To encourage them to make more sales, Wayne offered a $5,000 bonus to the salesperson who had the highest total dollar value the following month. That next month, Wendy had the highest sales. When Wendy received her next paycheck, there was no bonus. If Wendy sues Wayne to recover the $5,000 bonus, the likely result will be A. Wendy will lose because she already had a contract so there was no consideration B. Wendy will win because the offer of a bonus for high sales constituted consideration because it entailed additional performance by both parties C. Wendy will lose unless the promise was in writing. D. Wendy will win because of moral considerationIn the game of blackjack as played in casinos in Las Vegas, Atlantic City, and Niagara Falls, as well as in many other cities, the dealer has the advantage. Most players do not play very well. As a result, the probability that the average player wins a hand is about 45%. Find the probability that an average player wins. a.Twice in 5 hands. b. Ten or more times in 25 hands. Arrivals 0 1 2 3 4 5 6 7 8 Frequency 14 31 47 41 29 21 10 5 2In the signaling game represented below, there are two types of Player 1, smart and dumb, the probabilities of which are 0.4 and 0.6, respectively. Player 1 is in college and can either ((Q)uit or (G)raduate. Player 2 is a prospective employer and can either (N)ot hire or (H)ire Player 1. Player 2's payoff does not depend upon l's education, only her intelligence. Player 1's payoff depends partly on her education: both types benefit from completing their education, but the smart type gets more out of it. Player l's payoff also depends on 2's hiring decision: the smart type wants a job but the weak type does not. 0,0 1, 1 2, 1 0,0 N H N H 2 Q Q .4 C .6 18 G G N H H 2,0 3,1 3, 1 1,0 (a) Find a separating PBE. (b) Find a pooling PBE. (c) , Find an equilibrium in which one type of player 1 mixes, playing both Q and G with positive probability.