The payoff matrix for a game is 3 -3 4 -4 2 2 4 -5 2 (a) Find the expected payoff to the row player if the row player R uses the maximin pure strategy and the column C player uses the minimax pure strategy. (b) Find the expected payoff to the row player if R uses the maximin strategy 40% of the time and chooses each of the other two rows 30% of the time while C uses the minimax strategy 50% of the time and chooses each of the other two columns 25% of the time. (Round your answer to three decimal places.) (c) Which of these pairs of strategies is most advantageous to the row player? O (a) O (b)
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- Two friends, Khalid and Mahmood, are going to a watch a world cup football match. They play a simple game in which they hold out one or two fingers to decide who will pay for the other's ticket. Khalid wins if the fingers held out add up to an even number; Mahmood wins if the fingers held out add up to an odd number. The price of the ticket is 25 OMR. Construct a payoff matrix for the game. Is there a unique Nash equilibrium in this game? Which strategy should a player use to maximize her chances of winning the game?Brown’s TV Production is considering producing a pilot for a comedy series for a major network. While the network may reject the pilot and series, it may also purchase the program for 1 or 2 years. Brown may produce the pilot or transfer the rights for the series to a competitor for $100,000. Brown’s profits are summarized in the following payoff table (profits in thousands). sate of nature reject 1 year 2 years produce pilot -100 50 150 sell to competitor 100 100 100 If the probability estimates for the states of nature are, P(reject)=0.20, P(1 year)=0.30, and P(2 years)=0.5, what is the maximum Brown should be willing to pay for inside information on what the network will do?There are N>=2 collectors who engage in the auction of an antique. The collectorshave a common valuation of the antique, denoted by v, which is known to all. Thecollectors make a simultaneous bid. Let pn denote the bid by collector n = 1,....,N. The one with the highest bid wins the antique. The winner receives payoff v-pi.The other(s) receive zero payoff. If more than one collectors make the same highestbid, then they have an equal chance of winning the item. Prove that: A) It is not a Nash Equilibrium (NE) if the highest bid is v and onlyone collector bids this price.(b) It is not a NE if the highest bid is less than v.(c) It is a NE that the highest bid is v and more than one collector bidsthis price
- Assume that two collectors, X and Y are in a first prize sealed bid auction for a batch of vintage comic books. X and Y have different valuations (V) for this batch of comic books e.g. VX And VB are between $2000 and $4000. Both collectors know their own V but does not know the V of the other collector. All they know is that the other collector’s V is a uniformly distributed number between $2000 and $4000. Assume risk neutrality for X and Y e.g. expected payoff for X is: (VX – bX)Pr(bX) and expected payoff for Y is (VY – bY)Pr(bY). These collectors will make their bids strategically. Show how X’s bidding strategy is bX = ½ Vx + 1 and Y’s is bY = ½ Vy +1 in a Nash equilibrium.Two rival communications companies (Alpha and Beta) are both considering bringing out a revolutionary 8G wireless technology. Unfortunately, the costs of development are so high that the potential market could only support one firm. Both companies understand these possible outcomes. If one firm enters the 8G market and the other does not, the entering firm will receive $500 billion in profits over the next 5 years; the other firm will receive $100 billion over the same 5 years (by concentrating on their current 5G service). If neither enters the 8G field, they can both expect to receive $75 billion over the 5-year period, as they fight over the 5G market. Lastly, if both enter the 8G market, each will end up suffering a $50 billion loss over the same 5 years. Use a game table with “ENTER” and “STAY OUT” to decide each player’s options and the payoffs. Explain why each company has a strong reason to want to announce its intentions before the other company announces theirs.The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): state of nature low demand medium demnad high demand Decision alternative s1 s2 s3 manufacture d1 -20 40 100 purchase d2 10 45 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. a. Use expected value to recommend a decision. b. Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand.
- The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): state of nature low demand medium demnad high demand Decision alternative s1 s2 s3 manufacture d1 -20 40 100 purchase d2 10 45 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. a. A test market study of the potential demand for the product is expected to report either a favourable (F) or unfavourable (U) condition. The relevant conditional probabilities are as follows: P(F|S1)=0.10 P (U|S1)=0.90 P(F|S2)=0.40 P (U|S2)=0.60 P(F|S3)=0.60 P (U|S3)=0.40 A.Compute the probabilities by completing the table Sate of…The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): state of nature low demand medium demnad high demand Decision alternative s1 s2 s3 manufacture d1 -20 40 100 purchase d2 10 45 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. a. A test market study of the potential demand for the product is expected to report either a favourable (F) or unfavourable (U) condition. The relevant conditional probabilities are as follows: P(F|S1)=0.10 P (U|S1)=0.90 P(F|S2)=0.40 P (U|S2)=0.60 P(F|S3)=0.60 P (U|S3)=0.40 What is the expected value of the market research information?…The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): state of nature low demand medium demnad high demand Decision alternative s1 s2 s3 manufacture d1 -20 40 100 purchase d2 10 45 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. a. A test market study of the potential demand for the product is expected to report either a favourable (F) or unfavourable (U) condition. The relevant conditional probabilities are as follows: P(F|S1)=0.10 P (U|S1)=0.90 P(F|S2)=0.40 P (U|S2)=0.60 P(F|S3)=0.60 P (U|S3)=0.40 A.Compute the probabilities by completing the table Sate of…
- Consider a small town with two competing restaurants: Doug’s Diner and Betty’s Bistro. There is 1000profit to be made in the market. Each period, the restaurants simultaneously decide whether to offer high orlow quality food. In order to offer high quality food, each restaurant must hire an expert chef, which incursan additional cost of 100. The restaurants split the profit equally if they offer the same quality of food. Ifone restaurant offers high quality food while the other offers low quality food, the high quality restauranttakes four fifths of the profit and the low quality restaurant takes one fifth of the profit.(a) Draw up the normal form game matrix, showing the players, strategies, and payoffs.(b) Determine the Nash equilibrium of this game.(c) Explain how the restaurant owners could both be better off than in the Nash equilibrium if they wereable to cooperate. Is the town as a whole better off or worse off when the firms cooperate? Why or whynotThe first player can choose either U or D. If he chooses U, the second player has a choice of two strategies: L and R. If the second player moves L he obtains 1 and the first player gets 5. If the second player chooses R he obtains 2 units of payoff while the first player receives 1. Following a move D by the first player, both players engage in a simultaneous-move “Bach or Stravinsky” game (as it was described in class). Find the SPE of this game and write it down in a mixed and behavior form.The following profit payoff table was presented in Problem 1: The probabilities for the states of nature are P(s1) 5 0.65, P(s2) 5 0.15, and P(s3) 5 0.20.a. What is the optimal decision strategy if perfect information were available?