Country A is rich and country B is poor. Consequently, residents of country B want to immigrate to country A. The trouble is that there is no legal way to do. So they attempt to cross the border Illegally. There are 3 border crossings at which a resident of B may attempt to cross the border. An attempt is successful if there is no border guard at the crossing, and unsuccessful if there is a guard at the crossing. Country A has only 1 border guard. Model the game in which a resident of country B attempts to enter country A at one of the 3 border crossings, and the government of country A chooses to post its border guard at one of the 3 border crossings. In this game, each player has 3 pure strategies. A) What are the ultimate outcomes in this game? B) What are the player's Bernoulli Payoffs? C) Find a mixed strategy equilibrium of the game.

Country A is rich and country B is poor. Consequently, residents of country B want to immigrate to country A. The trouble is that there is no legal way to do. So they attempt to cross the border Illegally. There are 3 border crossings at which a resident of B may attempt to cross the border. An attempt is successful if there is no border guard at the crossing, and unsuccessful if there is a guard at the crossing. Country A has only 1 border guard. Model the game in which a resident of country B attempts to enter country A at one of the 3 border crossings, and the government of country A chooses to post its border guard at one of the 3 border crossings. In this game, each player has 3 pure strategies. A) What are the ultimate outcomes in this game? B) What are the player's Bernoulli Payoffs? C) Find a mixed strategy equilibrium of the game.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.10P

See similar textbooks

Similar questions

When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway. Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Valerie places a value of $15,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Valerie simply bids $15,000/2=$7,500 and wins the piece of art. The expected price paid by Valerie, with no other bidders present, is $________.. Suppose the owner of the artwork manages to recruit another bidder, Antonio, to the auction. Antonio is known to value the art piece at $12,000. The expected price paid by Valerie, given the presence of the second bidder Antonio, is $_______. .
Hansel has been making a cuckoo wristwatch, which he sells over the web. Customers are willing to pay $600 for Hansel’s watch, and each one costs him $240 to make. He has no fixed costs. Gretel is considering entry into this market. Her consultant has conducted a large-scale study of customers to determine how much they are willing to pay for watches of various quality levels. The consultant has found that customers’ willingness to pay equals 150q per watch, where q is a quality index the consulting firm has developed that ranges from 1 to 10. Gretel’s cost would be 15q2 per watch. Regardless of whether or not Gretel enters the market, and regardless of the quality level she chooses, Hansel will not change his competitive positioning. Suppose Gretel chooses to enter the market with a lower quality level to save on costs. Specifically, her quality index equals 3. What is her added value vis-à-vis Hansel (per watch)? What is the optimal quality level Gretel should choose…
Consider the experiment of a toss of two coins. A: observes one head.B: observes two heads. Find P(A) and P(B). Group of answer choices P(A) = 0.1 and P(B) = 0.2 P(A) = 0.25 and P(B) = 0.25 P(A) = 0.5 and P(B) = 0.25 P(A) = 0.25 and P(B) = 0.5 P(A) = 0.5 and P(B) = 0.5
Two identically able agents are competing for a promotion. The promotion is awarded on the basis of output (whomever has the highest output, gets the promotion). Because there are only two workers competing for one prize, the losing prize=0 and the winning prize =P. The output for each agent is equal to his or her effort level times a productivity parameter (d). (i.e. Q2=dE1 , Q2=dE2). If the distribution of “relative luck” is uniform, the probability of winning the promotion for agent 1 will be a function of his effort (E1) and the effort level of Agent 2 (E2). The formula is given by...Prob(win)=0.5 + α(E1-E2), where α is a parameter that reflects uncertainty and errors in measurement. High measurement errors are associated with small values of α (think about this: if there are high measurement errors, then the level of an agent’s effort will have a smaller effect on his/her chances of winning). Using this information, please answer the following questions. Both workers have a…
Two travelers on a plane have identical luggage and each contains an identical plate of rare china. Both plates are worth the same amount and only the two travelers know their true value. The airline loses both bags. The travelers are informed that the airline is liable to compensate them only up to $300. In order to determine an honest appraisal of the value of the plates, each traveler is taken to a separate room and asked to write down
The mayor of Green City is considering whether to institute a Covid vaccine mandate for public employees. The fire chief opposes vaccination, and has threatened to resign if a mandate is instituted. The mayor believes that instituting a mandate is critical to getting Covid under control, and thus not instituting the mandate would costs the city -50 utility. However, the fire chief is critical to maintaining public safety. If the fire chief resigns, it would cost the city 75 utility. The fire chief believes a mandate would be an invasion of his personal freedom, costing him 20 utility. The mandate only impacts the fire chief if he does not resign. However, resigning his job as fire chief would cost him 40 utility. Draw this game. Identify how many subgames it contains. Then, solve the game to find all subgame perfect Nash equilibria.
Two players bargain over 1 unit of a divisible object. Bargaining starts with an offer of player 1, which player 2 either accepts or rejects. If player 2 rejects, then player 1 makes another offer; if player 2 rejects once more, then player 2 makes an offer. If player 1 rejects the offer of player 2, then once more it is the turn of player 1 where he makes two consecutive offers. As long as an agreement has not been reached this procedure continues. For example, suppose that agreement is reached at period 5, it follows that player 1 makes offers in period 1,2 then player 2 makes an o er in period 3, then player 1 makes offers in 4,5. Negotiations can continue indefinitely, agreement in period 't' with a division (x, 1- x) leads to payoffs ( , (1-x)).(The difference from Rubinstein's alternating offer bargaining is that player one makes two consecutive offers, whereas player 2 makes a single offer in her turn.) a. Show that there is a subgame perfect equilibrium in which player 2's…
PLEAS ANSWER Q3 and Q4
A new government lottery has been announced. Each person who buys a ticket submits an integer between 0 and 100. The winner is the person whose submission is closest to four-fifths of the average of all submissions. If ties occur, the price will be shared. If Chloe expects other players to select numbers randomly, what number should she choose? Chloe should choose the number (a)_____ if you expect all other players to exhibit the same depth of reasoning as Chloe, what number would you choose? you should choose the number (b)______
Apple and Google are interested in hiring a new CEO. Both firms have the same set of final candidates for the CEO position: Indra, Cao, and Virginia. Both firms need to decide who to make a job offer to, and the hiring process is such that they each only make one job offer.If, say, Apple makes a job offer to Indra and Google makes a job offer to one of the other candidates, then Apple’s probability of success in hiring Indra is pIndra. The same is true for Google. If they both make a job offer to Indra, each has probability pIndra/2 of success. It has been estimated that pIndra = 20%, and pCao = pVirginia = 30% (Note that these probabilities need not add up to 100%).Suppose that both Apple and Google attach a valuation of 10 to successfully hiring Indra, and a valuation of 7 to successfully hiring each of the other candidates. A hiring attempt, if unsuccessful, has a valuation of zero. (a) Convert this story into a game by completing the following game table;GoogleIndra Cao…
Apple and Google are interested in hiring a new CEO. Both firms have the same set of final candidates for the CEO position: Indra, Cao, and Virginia. Both firms need to decide who to make a job offer to, and the hiring process is such that they each only make one job offer. If, say, Apple makes a job offer to Indra and Google makes a job offer to one of the other candidates, then Apple’s probability of success in hiring Indra is pIndra. The same is true for Google. If they both make a job offer to Indra, each has probability pIndra/2 of success. It has been estimated that pIndra = 20%, and pCao = pVirginia = 30% (Note that these probabilities need not add up to 100%). Suppose that both Apple and Google attach a valuation of 10 to successfully hiring Indra, and a valuation of 7 to successfully hiring each of the other candidates. A hiring attempt, if unsuccessful, has a valuation of zero. Convert this story into a game by completing the following game table; Google…
The residential division of Prism’s high-speed Internet service uses one advertising agency, while its commercial division uses another. Two analysts, Andy and Brad, are asked to test and evaluate the effectiveness of the two agencies. Andy proposes an A/B test that compares the click-through rates per ad for the two agencies. Brad proposes a difference-in-dif-ference test in which the budgets for both agencies are increased by 50%, and the percent change in click-through rates is compared. What might be the sources of selection bias for the two proposals? Which is likely to be smaller?