Assume that the effective security level is now determined by the highest (not the lowest) security measures chosen by airlines. Letting max{s1, . . . , sn} denote the highest of the airlines’ strategies, we find that airline i’s payoff is now 50 + 20 x max{s1, . . . , sn} -10 si. Assuming the same strategy sets, find all Nash equilibria.
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Assume that the effective security level is now determined by the highest (not the lowest) security measures chosen by airlines. Letting max{s1, . . . , sn} denote the highest of the airlines’ strategies, we find that airline i’s payoff is now
50 + 20 x max{s1, . . . , sn} -10 si.
Assuming the same strategy sets, find all Nash equilibria.
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- Several firms collude in an oligopoly where the Industry Supply is given by QS = 6 - 5P and Industry Demand is given by, QD = 5P – 5. If the probability that this collusion will continue is given by (1/P*), what is the minimum number of firms required to break the tacit collusion?Consider a sealed-bid auction in which the seller draws one of the N bids at random. The buyer whose bid was drawn wins the auction and pays the amount bid. Assume that buyer valuations follow a uniform(0,1) distribution. 1. What is the symmetric equilibrium bidding strategy b(v)?2. What is the seller’s expected revenue?3. Why doesn’t this auction pay the seller the same revenue as the four standard auctions? That is, why doesn’t the revenue equivalence theorem apply here?Return to the Lemons game, and consider the same structure, except suppose there are just two quality levels: low and high. The buyer initially assigns probability q to a car’s being of high quality and probability 1 - q to its being of low quality. If the seller sells the car, then her payoff is the price the buyer paid. If the car is not sold, assume that it is worth $10,000 to the seller if it is of high quality and $6,000 if it is of low quality; those are the payoffs. The value of the car to the buyer is $12,000 if it is of high quality and $7,000 if it is of low quality. If the buyer purchases the car, then the buyer’s payoff is the car’s value—which is $12,000 or $7,000—less the price paid; his payoff is zero if he does not buy the car. Find values for q such that there is a PBNE with pooling.
- You are a bidder in an independent private values auction, and you value the object at $4,500. Each bidder perceives that valuations are uniformly distributed between $500 and $9,000. Determine your optimal bidding strategy in a first-price, sealed-bid auction when the total number of bidders (including you) is: a. 2 bidders.Bid: $ b. 10 bidders.Bid: $ c. 100 bidders.Bid: $Consider the game in the image attached, which is infinitely repeated at t = 1, 2, ... Both players discount the future at rate: delta E(0, 1). The stage game is in the image attached. Suppose that the players play (C,C) in period t = 1, 3, 5, ... and plays (D,D) in period t = 2, 4, 6,... Compute the discounted payoff of each player.Is the following statement true? "5 bidders with private values uniformly distributed between 0 and 1 enter a 1st price auction. Assuming that everyone is playing the symmetric equilibrium bidding strategy, the optimal bid for a bidder who makes a draw of 0.75 is 0.7."
- Consider a Common Value auction with two bidders who both receive a signal X that is uniformly distributed between 0 and 1. The (common) value V of the good the players are bidding for is the average of the two signals, i.e. V = (X1+X2)/2. Compute the symmetric Nash equilibrium bidding strategy for the second-price sealed-bid auction assuming that players are risk-neutral and have standard selfish preferences. Furthermore, you may assume that the other bidder is following a linear bidding strategy. Make sure to explain your notation and the steps you take to derive the result.For each of the following scenarios, determine whether the decision maker is risk neutral, risk averse, or risk loving.a) A manager prefers a 10 percent chance of receiving $1,000 and a 90 percent chance of receiving $100 to receiving $190 for sure.b) A shareholder prefers receiving $775 with certainty to a 75 percent chance of receiving $1,000 and a 25 percent chance of receiving $100.c) A consumer is indifferent between receiving $550 for sure and a lottery that pays $1,000 half of the time and $100 half of the time.Two firms, A and B, know that holder of a telecom license will make a profit of either £0 or £4m with equal probabilities. They bid simultaneously either £0 or £1m for this license. The highest bidder wins the license (with probability ½ if both bidders submit the same bid) and pays its bid. a) Represent the game in normal and extensive form. b) Solve the game with the relevant solution concept(s). c) Represent the game in normal and extensive form when, before bidding, firm A learns the actual profit (£0 or £4m) of the license holder. d) Solve the game in c) with the relevant solution concept(s). Does firm A benefit from learning the actual profit?
- For each of the following scenarios, determine whether the decision maker is risk neutral, risk averse, or risk loving. a. A manager prefers a 20 percent chance of receiving $1,400 and an 80 percent chance of receiving $500 to receiving $680 for sure. b. A shareholder prefers receiving $920 with certainty to an 80 percent chance of receiving $1,100 and a 20 percent chance of receiving $200. c. A consumer is indifferent between receiving $1,360 for sure and a lottery that pays $2,000 with a 60 percent probability and $400 with a 40 percent probability.1 \ 2 a b c A 2,2 2,1 0,0 B 3,1 3,0 1,3 C 1,3 3,2 3,1 a) Eliminate iteratively all strictly dominated strategies. b) Find all Nash equilibria. c) What is the player 1’s best response to the strategy σ2 = (z , ½ , ½ - z) of player 2, where z is a parameter that lies in the closed interval [0, ½]. d) Compute the payoffs to player 1 and to player 2 for their respective strategy profiles σ1 = (0,½,½) and σ2 = (½,0,½).1. Find best responses of one of the firms to the strategies of its counterpart. Which of the strategies is not a best response to any pure strategy? 2. Let firm 2 play strategies (0, 1, 2) with probabilities (q1, q2, q3), q1 +q2 +q3 = 1. Calculate the expected payoff of firm 1 from playing each of the three strategies. Show that the strategy which is not the best response to any pure strategies is strictly dominated by the other two strategies if firm 2 plays mixed strategies.