Cheetah Air and Eagle Air are comper industry. First, Cheetah Air decides w service to Maul or not. Then, Cheetal demand for the air service is high or la about the market spills over to Eagle demand will be high with probability 6 40%. After observing the market dema does enter or stay out. This situation
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- 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…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, 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 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. 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 35
- Consider a situation of after-match penalty shoot-out. The striker can target either East or West side of the goal. If he targets West, with 80% chance he shoots on target. If he shoots East, he is accurate with 75%. The goalkeeper has to choose the corner to jump to. If he does not guess the corner correctly and the shot is on target, then the striker scores. If the striker shoots West, the shot is on target and the goalkeeperjumps West, then with 75% chance he saves the goal. If the striker shoots East, the shot is on target and the goalkeeper jumps East, then with chance of 2/3 he saves the goal. Suppose, that it is a zero-sum game and if the striker scores his payoff is 1, otherwise it is 0.1. Formulate this situation as a strategic game and Find all Nash equilibria of the game.Player 1 L 20, 12 4,8 10, 2 6,6 R 0, 14 8,4 2,18 6,6 ). If 1 believes that 2 plays a mixed strategy (0.25, 0.75), i.e. with 25% probability of L and 75% probability of R, which of 1's strategies has the highest expected payoff? N E S W N E S W Player 2 2. If 2 actually plays a mixed strategy (0.25, 0.75), i.e. with 25% probability of L and 75% probability of R, which of 1's strategies would give 2 the highest expected payoff? N E S WQuestion 2. In an industry, there is an incumbent firm (Firm 1) and there is a potential entrant firm (Firm 2). Firm 1 decides whether to build a new plant, and simultaneously Firm 2 decides whether to enter into this industry. The cost of building a new plant for Firm 1 can be high or low, which is Firm 1's private information. Firm 2 is uncertain about Firm 1's cost, and believes that with probability TE [0, 1] the building cost for Firm 1 is high, and low with probability 1-7. The payoffs are depicted below. Build Not Build Enter 0, -1 2,1 Not Enter 2,0 3,0 High Cost Build Not Build 1 Enter 1.5, -1 2,1 Not Enter 3.5,0 3,0 Low Cost This interaction comprise a Bayesian game. Firm 2 does not know the matrix in which they are in, but Firm 1 does now it. As we have seen in class, there are 5 things that define this Bayesian game. 1. Set of players: N {Firm 1, Firm 2}. = 2. Set of actions for each player: A₁ = {Build, Not Build}, A2 3. Type space of Firm 1: ₁ = {H, L}. {Enter, Not Enter}.…
- Consider the following game. Player S DE F A 10, 10 8, 7 8, 8 Player R B 8,7 9, 8 9, 12 C 9,8 7, 10 12, 7 Find the best response of step-2 Player S assuming that step-0 players (either Ror S) choose the strategy at random with equal probability. Select one: O a. F O b. E O c. B O d. A O e. C O f. D"Jay, a writer of novels, just has completed a new thriller novel. A movie company and a TV network both want exclusive rights to market his new title. If he signs with the network, he will receive a single lump sum of $1,480,000, but if he signs with the movie company, the amount he will receive depends on how successful the movie is at the box office.The probability of a small box office earning $203,000 is 0.27. The probability of a medium box office of $1,660,000 is 0.49, and the probability of a large box office of $2,950,000 is 0.24.Jay can send his novel to a prominent movie critic to assess the potential box office success. It will cost $20,000 to get the novel evaluated by the movie critic.The movie critic can have either a favorable or unfavorable opinion. The movie critic's reliability of predicting box office success is as follows.If the movie will have a large box office, there is a 0.75 probability the critic will have a favorable opinion.If the movie will have a medium…Boris and Angela are negotiating a new trade deal, which resembles a modified centipede game. When it is their turn, each of them decides whether to cooperate (C) or to decline (D). Unfortunately, Angela is not sure how much time Boris has for the negotiations before he needs to leave to talk to Emmanuel. With probability p = 4/5, Boris will stay and insist on making the final proposal (long game, L). With probability 1 − p = 1/5, Boris will have to rush off, so that the game ends after Angela’s move (short game, S). Boris has perfect knowledge of his schedule. The structure and payoffs are represented in the game tree below (Attached picture). (a) Specify the set of possible histories H of the game. Underline terminal histories.(b) Specify the set of possible strategies for Boris and Angela.(c) How many subgames does this game have? Indicate all subgames in this game
- 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.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…At races, your horse, White Rum, has a probability of 1/20 of coming 1st, 1/10 of coming 2nd and a probability of 1⁄4 in coming 3rd. First place pays $5,000 to the winner, second place $4,000 and third place $1,350.Hence, is it worth entering the race if it costs $1050? Your company plans to invest in a particular project. There is a 40% chance you will lose $3,000, a 45% chance you will break even, and a 15% chance you will make $5,500. Based solely on this information, what should you do? On 1st Jan 2006, a business had inventory of $19,000. During the month, sales totalled $32,500 and purchases $24,000. On 31st Jan 2006 a fire destroyed some of the inventory. The undamaged goods in inventory were valued at $11,000. The business operates with a standard gross profit margin of 30%. Based on this information, what is the cost of the inventory destroyed in the fire?