Film producer S costs c=20 to produce one film. B, an online movie distributor, earns v=120 if the movie is distributed. In order for B to distribute the movie, it must be purchased from S. If there is no transaction between S and B, each earns a profit of zero. Find the sum of S's profit and B's profit by the transaction price formed when S and B's bargaining power is 50:50.
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2.
Film producer S costs c=20 to produce one film. B, an online movie distributor, earns v=120 if the movie is distributed. In order for B to distribute the movie, it must be purchased from S. If there is no transaction between S and B, each earns a profit of zero.
Find the sum of S's profit and B's profit by the transaction price formed when S and B's bargaining power is 50:50.
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- Splitting Pizza: You and a friend are in an Italian restaurant, and the owner offers both of you a free eight-slice pizza under the following condition. Each of you must simultaneously announce how many slices you would like; that is, each player i ∈ 1, 2 names his desired amount of pizza, 0 ≤ si ≤ 8. If s1 + s2 ≤ 8 then the players get their demands (and the owner eats any leftover slices). If s1 + s2 > 8, then the players get nothing. Assume that you each care only about how much pizza you individually consume, and the more the better.What outcomes can be supported as pure-strategy Nash equilibria?Mary and Raj are the only two growers who provide organically grown corn to a local grocery store. Table below represents the choices available to Mary and Raj and the payoffs associated with each outcome. What is the best choice for Raj if he is sure that Mary will cooperate? If Mary thinks Raj will cheat, what should Mary do and why? What is the prisoner’s dilemma result? (A = Work independently; B = Cooperate and Raise prices. Each results entry lists Raj earnings first, and Mary's earnings second.) Mary A B Raj A ($100, $100) ($200, $0) B ($0, $200) ($150, $150)high low high 11, 11 2,18 low 18, 2 10,10 Suppose there are only two firms that sell tablets: Padmania and Capturesque. The following payoff matrix shows the profit (in millions of dollars) each company will earn, depending on whether it sets a high or low price for its tablets. For example, the lower-left cell shows that if Padmania prices low and Capturesque prices high, Padmania will earn a profit of $18 million, and Capturesque will earn a profit of $2 million. Assume this is a simultaneous game and that Padmania and Capturesque are both profit-maximizing firms. If the firms do not collude, what strategies will they end up choosing? 1. Padmania will choose a low price, and Capturesque will choose a high price. 2. Both Padmania and Capturesque will choose a high price. 3. Padmania will choose a high price, and Capturesque will choose a low price. 4. Both Padmania and Capturesque will choose a low price. True or False: The…
- Two parties, Juan and Ben, have been negotiating the purchase by Ben of Juan's car. Juan receives a new and higher bid for his car from Adriana. How might Adriana's bid change Juan and Ben's threat values? The threat values are unchanged. Juan now values the car at the price of Adriana's bid, her bid is his opportunity cost of selling the car to Ben, and that opportunity cost is Juan's new threat value. Juan's new threat value is the product of the difference between Ben and Adriana's offers and the probability the car will be sold to Adriana. Juan's threat value is unchanged, but Ben has to consider his new opportunity cost2 clothing manufacturers, LE and LL B, are deciding what price to charge for very similar field coats. Cost of producing these coats is $100. The coats are very close substitutes, so customers swarm to the seller that offers the lowest price. If both firms offer the same prices, each receives half of the customers. Assume the two firms have the choice of pricing at prices of $103, $102, or $101. The profit each firm would earn at various prices is shown in the payoff matrix below $103 ($150, $150) ($0, $200) ($0, $120) Lands' End $102 ($200, $0) ($100, $100) ($0, $120) $101. ($120, $0) ($120, $0) ($50, $50) What is the Nash equilibrium and expected profits to LLB and LE of this game? If this was a mixed strategy game in which LLB has a 25% percent chance of choosing a price of $101, a 25% chance of choosing price of $102, and a 50% chance of choosing $103, while LE has a1/3 chance of…Consider the bargaining problem of splitting a pie of size 1 with utility u(x1) = x1 for player 1 and v(x2) = 2x2 − x22 for player 2, where x1 and x2 denote the share of the pie for player 1 and 2 respectively. a) Consider the bargaining problem of the two players. Find the utility possibility frontier S. b) What is the Nash bargaining solution for this problem (i.e., on which division of the pie (?₁,?₂) will players agree), if the disagreement outcome (the utilities players obtain in case of disagreement) is d1 = d2 = 0? c) What is the Nash bargaining solution if the disagreement outcome is any d1 and d2 in S?
- Consider the following representation of a Normal form game. actions w a (45,22) (10,38) (42,13) (10,7) (p,28) (15,40) (q,10) (44,10) (20,22) (14,31) (27,13) (12,8) d. (20,41) (9,48) (28,24) (18,32) Here each cell in the table represents an ordered pair. First element is payoff of the first player and second element is payoff of the second player. The letters a, b, c, d, x, y, z, w represent the actions. Write down the table in your answer script too. Now answer the following questions: 1. What is the distinction between strictly dominant strategy and weakly dominant strategy? Is it reasonable for a player to play a strictly dominated strategy? Explain why. 2. What are the minimum values for p and q that will make ba strategy that strictly dominates all other strategies for player 1, assuming both p and q are natural numbers? 3. Does player 2 have any strictly dominated pure strategy? If yes, which pure strategy dominates that strategy? If the submit button is off it is beacuse the due…5) Three legislators are set to vote on a bill to raise the salary of legislators. The majority wins, so all three will receive the raise if at least two of them vote in favor of the bill. The raise is valued at R by each legislator. Voting in favor of the bill comes with political backlash from constituents, though, even if the bill fails. Let C be the cost of backlash for anyone voting in favor of the bill. Finally, suppose that 0 < C < R. There are four possible payoffs for each legislator: 0: if they vote against the bill and at least one other legislator votes against it (so the bill fails) R: if they vote against the bill and the others vote for the bill (so the bill passes) -C: if they vote for the bill and no one else votes for the bill (so the bill fails) R-C: if they vote for the bill and at least one other legislator votes for it (so the bill passes). The three legislators are named X, Y, and Z, and voting happens sequentially and orally. So X announces their vote (to…Suppose a $1 bill is to be divided between two players according to a simultaneous-move, one-shot bargaining game. Is there a Nash equilibrium to the bargaining game if the smallest unit in which the money can be divided is $0.01? Assume that if the players ask for more in total than is available, they go home empty-handed.
- Suppose that total unit sales of iPhones and Android phones depends on both Apple’s and Google’s advertising expenditures: Google Advertise Don’t Apple Advertise 100, 100 120, 60 Don’t 60, 120 80, 80 To find the firm’s profits from the sales figures, assume that the price is $30, that the marginal cost is $20, and that the fixed cost of advertising is $300. (a) Fill in the profits in the following simultaneous-move game: Google Advertise Don’t Apple Advertise ? ? Don’t ? ? (b) What is the Nash equilibrium of the game? What strategies result in thehighest industry profits? Explain in words why the firms don’t choosethose strategies?Again consider an extension of the Stag Hunt game. There are N = 3 hunters. This time each hunter has multiple effort levels in hunting for stag. Specifically, assume each hunter i can choose effort level ei = 0, 1, 2, 3, 4. Given a strategy profile (e1, e2, e3), each player i 0 s payoff = 2 min{e1, e2, e3} − ei . In words, payoff equals twice of the least effort level of everyone subtract player i’s own effort level. For example, if player 3 chooses e3 = 1, players 1 and 2 both choose effort level 4 then the minimum effort level min{e1, e2, e3} = 1, so player 3’s payoff equals 2 × 1 − e3 = 1 and players 1 and 2 each gets payoff 2 × 1 − 4 = −2. a. Is a strategy profile in which all players choose the same effort level a Nash equilibrium? Explain. (Consider what a player’s payoff is given this profile and what payoff he could get by increasing or decreasing his effort.) b. Is any profile in which not all effort levels are equal a Nash equilibrium? Explain.12.3 Armed Conflict: Consider the following strategic situation: Two rival armies plan to seize a disputed territory. Each army's general can choose either to attack (A) or to not attack (N). In addition, each army is either strong (S) or weak (W) with equal probability, and the realizations for each army are independent. Furthermore the type of each army is known only to that army's general. An army can capture the territory if either (i) it attacks and its rival does not or (ii) it and its rival attack, but it is strong and the rival is weak. If both attack and are of equal strength then neither captures the territory. As for payoffs, the territory is worth m if captured and each army has a cost of fighting equal to s if it is strong and w if it is weak, where s <w. If an army attacks but its rival does not, no costs are borne by either side. Identify all 12.7 Exercises • 267 the pure-strategy Bayesian Nash equilibria of this game for the following two cases, and briefly describe…