In a small isolated town, there are two types of people, saints and crooks. In business dealings between any two residents of this town, the payoffs are below. Saint Crook Saint 7,7 0, 10 Crook 10, 0 -5,-5 What percentage of this town's residents would be saints in an evolutionary stable strategy? a) 62.50% b) 0% c) 15.30% d) 100% e) 87.50%
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- A6. 1.Adam and Zoey are competing fish and chips sellers in Linear City. They are located at the twoopposing ends of the town’s 3-mile-long Main Street. The 1700 inhabitants of the town are distributeduniformly on Main Street and each of them eats at most one portion of fish and chips for lunch. People’sdisutility from getting to a fish and chips stand and back home amounts to $2 for each mile of distanceto the stand. The marginal cost of producing one portion of fish and chips is $9. The consumers areuniformly distributed along the street. Each consumer has a valuation of $29.0 for the product. Supposethat both Zoey and Adam can advertise at zero cost to inform everyone about their business. Find theequilibrium price of Zoey if neither of the two sellers advertises.Someone at a party pulls out a $100 bill and announces that he is going to auction it off. There are n=10 people at the partywho are potential bidders. The owner of the $100 bill puts forth the following procedure: All bidders simultaneously submit a written bid. Only the highest bidders pay their bid (assuming that the highest bid is positive). If m people submit the highest bid, then each receives 1/m of the $100. Each person’s strategy set is {0,1,2,...,1000}{0,1,2,...,1000} so bidding can go as high as $1,000. The payoff of a player bidding bi is:0 if bi < max{b1,b2,…,bn},and 100/m − bi if bi = max {b1,b2,…,bn}where,m is the number of bidders whose bid equals max{b1,...,bn}. How many pure-strategy Nash equilibria does this game have? 1) 0 2) 1 3) 4 4) More than 4.Describe the payoffs for an R&D game of chicken and contrast them with the payoffs in a prisoners' dilemma game. The outcome is that In the prisoners' dilemma R&D game, a firm can use the R&D O A. if either it or its competitor conducts the R&D; one firm conducts R&D; B. only if it conducts the R&D; one firm conducts R&D; OC. If either it or its competitor conducts the R&D; neither firm undertakes R&D; D. only if it conducts the R&D; both firms undertake R&D; In an R&D game of chicken, a firm can use the R&D The outcome is that A. only if it conducts the R&D; one firm conducts R&D B. only if it conducts the R&D; both firms undertake R&D C. if either it or its competitor conducts the R&D; one firm conducts R&D D. If either it or its competitor conducts the R&D; both firms undertake R&D
- 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 whynot?The prisoners’ dilemma is a two-person gameillustrating thata. the cooperative outcome could be worse for bothpeople than the Nash equilibrium.b. even if the cooperative outcome is better thanthe Nash equilibrium for one person, it might beworse for the other.c. even if cooperation is better than the Nashequilibrium, each person might have an incentivenot to cooperate.d. rational, self-interested individuals will naturallyavoid the Nash equilibrium because it is worsefor both of them.In game theory, a dominant strategy is the best strategy to pick, no matter which moves are chosen by the other player. O to make the exact same move that was made by the other player. the choice that causes the payoff for the other player to be minimized, regardless of the payoff it earns the best strategy to pick, assuming the other player makes his or her best possible choice. to allocate all personnel resources towards defensive talent in order to dominate opposing offenses. 46°F
- There are a kicker and a goalie who confront each other in a penalty kick that willdetermine the outcome of the game. The kicker can kick the ball left or right, while the goaliecan choose to jump left or right. Because of the speed of the kick, the decisions need to bemade simultaneously. If the goalie jumps in the same direction as the kick, then the goalie winsand the kicker loses. If the goalie jumps in the opposite direction of the kick then the kickerwins and the goalie loses. Model this as a strategic form game and write down the matrix thatrepresents the game you modeled. Find the Nash equilibrium.The next 3 questions involve the following game. There are two players, a husband and wife. They can either be selfish (S) or selfless (U) in their marriage. If they choose to be selfish, then there is a negative ʻguilt’ payoff of g. The payoff matrix is below. Figure 1: The Marriage Game Wife S U S 10-g, 10-g 15-g, 2 U 2, 15-g 12, 12 Number left (right) of comma refers to H's (W's) payoff. 23. Suppose that g = 0. What is the Nash equilibrium (or equilibria)? (A) (S, S). (B) (U, S) and (S, U). (C) (S, S) and (U, U) (D) (U, U). 24. Suppose that g= 5. What is the Nash equilibrium (or equilibria)? (A) (S, S). (B) (U, S) and (S, U). (C) (S, S) and (U, U) (D) (U, U). 25. Suppose that g = 10. What is the Nash equilibrium (or equilibria)? (A) (S, S). (B) (U, S) and (S, U). (C) (S, S) and (U, U) (D) (U, U). HusbandThe Dean of a College is looking for a tenured professor to teachin the Core Curriculum. Monetary incentives are needed to get someoneinterested, but how much? The Dean decides to use an auction to do thejob. Two professors, equally qualiÖed, applied for the position. The twoprofessors are invited to covertly submit their bids to the Dean. The Deanwill give the position to the professor who submits the lower bid (if thereis a tie, the job is assigned randomly). The professor who gets the job willbe paid his/her own bid. Each professorís reservation value for teachingthe course is his/her private information. It is common knowledge thattheir reservation values are independently and uniformly distributed over[0;100]: So if a professor with a reservation value of 60 wins with a bid of50, his payoff is 60- 50 = 10: (A) Find a Bayesian Nash equilibrium of the bidding game.(B) Suppose the two professorsíreservation values are 60 and 70, respectively. What are their bids in the Bayesian Nash…
- b. Two farmers, Anil and Bala, are each deciding how to deal with pest insects that destroy the crops they cultivate in their adjacent fields. They have the choice of using either Integrated Pest Control (IPC) or Terminator (T). The payoffs for their choices, in terms of tonnes of crop, are as follows: Bala's payoff 5 4 3 1 0 0 I, T 1 T, T: 1,1 2 3 Anil's payoff 4 T, I 5 Outcomes better for both than I, I Outcomes better for both than T, T Outcomes better for both than T, I Outcomes better for both than I, T I, I = Both use Integrated Pest Control (IPC) T, T = Both use Terminator T, I Anil uses Terminator, Bala uses IPC I, T = Anil uses IPC, Bala uses Terminator i. Define what is meant by a 'Pareto efficient outcome. Which of the four outcomes shown above are Pareto efficient? T) to the "fairer" ii. Will Anil and Bala both be happy to move from the Pareto efficient Pareto efficient outcome (I, I)? What does your answer to this question tell us about the link between equity and Pareto…L 0 4 15.1 X₂ A M R 0 1 4 0 2 B L 4 0 с X3 M R 0 1 3 FIGURE 15.5 Exercise 15.1. Equilibrium Selection: Consider the extensive-form game in Figure 15.5. a. Find all the Bayesian Nash equilibria of this game. b. Which of the Bayesian Nash equilibria are also perfect Bayesian equi- libria? Why?The prisoners' dilemma is a two-person game illus·trating thata. t he cooperative outcome could be worse for bothpeople than t he Nash equilibrium.b . even if the cooperative outcome is better than theNash equilibrium for one person, it might be worsefor the other.c. even if cooperation is better than the Nash equilibrium,each person might have an incentive not tocooperate.d . rational, seff·interested individuals will naturallyavoid the Nash equilibrium because it is worse forboth of them.