Edgar Allan Melville is a successful novelist who is negotiating a contract for a new novel with his publisher, Potboiler Books, Inc. The novelist's contract strategies encompass various proposals for royalties, movie rights, advances, and the like. The following payoff table shows the financial gains for the novelist from each contract strategy: Novelist Strategy 1 2 3 A $80,000 130,000 110,000 Publisher Strategy B $120,000 90,000 140,000 C $90,000 80,000 100,000 a. Does this payoff table contain any dominant strategies? b. Determine the strategy for the novelist and the publisher and the gains and losses for each.
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- Does each individual in a prisoners dilemma benefit more from cooperation or from pursuing self-interest? Explain briefly.1. Consider the pricing game between firm 1 (row) and firm 2 (column) belowwhere each number represents the profits made by each firm.:Table 1: Pricing gameLow HighLow 288,288 360,216High 216,360 324,324 a) Point out the Nash equilibrium. Is this a unique Nash equilibrium?c) What type of commitment can firm 1 make to improve its pay-off?Can it be classified as a threat or promise? (Assume that the commitmentis credible.)d) How would you represent the game as a game tree with the option tocommit?2. Consider the signalling / production game with the order of play given below.Assuming that the signal is informative (i.e. education is sufficiently costly),how would you change the order of the game to make sure that poolingequilibriums are ruled out? Verbally motivate your answer.• Nature chooses ability of the workers a ∈ (H, L), ability is observed byworkers but not employers.• The worker choose an education level s ∈ (0, 1).• The employer offer contracts w(s).• The worker accepts or…3. Suppose that the various Balls of basketball or internet fame Lavar, Lamelo, Liangelo, Lonzo,and Spalding are considering playing in a 1-on-1 tournament. They get a payoff of 0 if theydecide not to participate. The following table illustrates their payoffs across the variousscenarios. 1 Player 2 Players 3 Players 4 Players 5 Players Lavar 10 4 2 -2 -5 Lamelo 10 7 5 2 -1 Liangelo 10 7 5 2 -1 Lonzo 10 8 7 6 5 Spalding 10 9 8 7 6 a. Find and describe all pure strategy Nash Equilibria.b. Suppose now Spalding, since it is in fact a literal basketball, gets a payoff of 0 in anycircumstance, being an inanimate object. The table is now as follows: 1 Player 2 Players 3 Players 4Players 5 Players Lavar 10 4 2 -2 -5 Lamelo 10 7 5 2 -1 Liangelo 10 7 5 2 -1 Lonzo 10 8 7 6 5 Spalding 0 0 0 0 0 Find and describe all pure strategy Nash Equilibria.
- 12. Consider a game where each player picks a number from 0 to 60. The guess that is closest to half ofthe average of the chosen numbers wins a prize. If several peopleare equally close, then they share theprize. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 (C) there is a Nash equilibrium where all players pick 0 (D) there is a Nash equilibrium where all players pick positive numbers 13. Behavioral data in such games suggests that (A) most subjects choose 0; (B) most subjects choose 30; (C) common answers include 30, 15, 7.5, and 0; (D) most subjects use randomization. Can you help me answer number 13 please?1) What are the Nash equilibria? Which one is unreasonable/non-credible threat? 2) What are the subgame perfect Nash equilibria? Does SPNE concept eliminate the unreasonable Nash equilibrium?Game Theory a) Consider the following game represented by the game tree below. If you observe Blue Bank playing medium and Green Bank playing bottom, would you be surprised by their choices? Carefully explain why or why not. b) Now assume that Blue and Green Banks play the game with the same actions and payoffs as in a) but they make their choices simultaneously. What is the payoff matrix for this new game? What do you predict will happen in the game? Explain. c) Assume that the game from part a) is played five times, i.e. Blue and Green Banks play a repeated game with the stage game described in a). What do you predict will happen in the game? Explain.
- please discuss the separation eqilibrium in details 1. Assume that two players play the Tinder game. There are two types of potential boyfriends: the gentleman (25% of the population) and the douchebag (75% of the population), and they can decide on the different level of effort: low, medium, and high. For the first type, the respective costs are 30, 50, and 80. For the second type, the respective costs are 50, 75, and 120. For the potential boyfriend, the payoff from being in relationship is 130, and the payoff associated with being dumped is 70. The girl can get 60 if she stays single, 100 if she is in relationship with the gentleman, and 25 if she dates the douchebag (credits to Owen Sims) a) Present the game in the extensive form b) Calculate the expected pay-off for the girl. Should she date at all? c) Discuss whether the game has a separating equilibriumConsider the following price game: Firm 1 Firm 2 High Low High 20, 20 12, 24 Low 24, 12 14, 14 Remark: In simultaneous move games (games with rows and columns) theconvention is to write the row player’s payoff first and the column player’spayoff second. (a) What is the Nash equilibrium of this game? Recall that for each playeryou should find the best response to each of the opponents’ strategies andunderline the associated payoff. Then look for a cell where both strategiesare best responses to each other. This is a Nash equilibrium. (b) Does either firm have a dominate strategy (a strategy that is always abest response)?5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:A writes down either number 1 or number 2, and B must guess which one.If the number that A has written down is i and B has guessed correctly, B receives i units from A.If B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.Suppose B guesses 1 with probability p and 2 with probability 1 −p.Let X1 denote B’s gain (or loss) in a game where A has written down 1.Let X2 denote B’s gain (or loss) in a game where A has written down 2.(a) Find the pmf of X1 and X2(b) Find B’s expected gain for these two cases, E[X1] and E[X2].(c) What value of p maximizes the minimum possible value of B’s expected gain?Now consider the expected loss of player ASuppose that A writes down 1 with probability q and 2 with probability 1 −q.Let Y1 be A’s loss (or gain) if B chooses number 1.Let Y2 be A’s loss (or gain) if B…
- 6)Game Theory: The Prisoners’ Dilemma: Assume that the Wilson and Spalding athletic equipment companies are in a one-shot game for market share and profits, but that they have the option of choosing only one of two possible price strategies for basketballs: $20 or $80. Obviously if they choose different strategies, the firm with the lower price will win the entire market. The firms face the following payoff matrix (See Chap. 10). Wilson\ \Spalding Wilson $ 20 Price Wilson $ 80 Price Spalding $ 20 Price $ 400, $ 400 $ 1500, $ 0 Spalding $ 80 Price $ 0, $ 1500 $ 1000, $ 1000 What strategy will each firm choose? Why? Which strategy is dominant? Which strategy is preferred by each firm? What will be the outcome of the one-shot game? Where is the Nash equilibrium? Which outcome would be best for the two firms? What will happen if the game is repeated an infinite number of times?Consider trade relations between the United States and Mexico. Assume that the leaders of the two countries believe the payoffs to alternative trade policies are shown in the image attached. a) What is the dominant strategy for the United States? For Mexico? Explain. b) Define Nash equilibrium. What is the Nash equilibrium for trade policy? c) In 1993, the U.S. Congress ratified the North American Free Trade Agreement, in which the United States and Mexico agreed to reduce trade barriers simultaneously. Do the perceived payoffs shown here justify this approach to trade policy? Explain.1. Ten commuters must decide simultaneously in the morning to use route A or route B to go from home (same place for all) to work (ditto). If a of them use route A, each of them will travel for 10a + 40 minutes; if b of them use route B, each of them will travel for 10b minutes. Everyone wishes to minimize his/her commuting time. a) Describe the pure Nash equilibrium (or Nash equilibria) of this ten-person game. Compute the corresponding profile of commuting times. Explicitly list all equilibrium conditions that are satisfied.