Firms A and B are contemplating whether or not to invest in R&D. Each has two options: “Invest” and “Abstain.” A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn’t invent X, it makes $0 in revenue. If a firm invests and is the only one to invent X, it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other’s investment decisions. The “research and development” game is best analyzed as a simultaneous move game, because the parties lack information about each other’s investment decisions. Find the Nash Equilibria (or Equilibrium) of the “research and development” game. A) There are no Nash EquilibriaB) Invest / InvestC) Invest / Abstain, and Abstain / InvestD) Abstain / AbstainE) None of the above

Firms A and B are contemplating whether or not to invest in R&D. Each has two options: “Invest” and “Abstain.” A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn’t invent X, it makes $0 in revenue. If a firm invests and is the only one to invent X, it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other’s investment decisions. The “research and development” game is best analyzed as a simultaneous move game, because the parties lack information about each other’s investment decisions. Find the Nash Equilibria (or Equilibrium) of the “research and development” game. A) There are no Nash EquilibriaB) Invest / InvestC) Invest / Abstain, and Abstain / InvestD) Abstain / AbstainE) None of the above

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter18: Asymmetric Information

Section: Chapter Questions

Problem 18.1P

See similar textbooks

Similar questions

Firms A and B are contemplating whether or not to invest in R&D. Each has two options: “Invest” and “Abstain.” A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn’t invent X, it makes $0 in revenue. If a firm invests and is the only one to invent X, it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other’s investment decisions. What is Firm A’s expected gross revenue (i.e., not net of investment costs) from investing, assuming Firm B invests (i.e. conditional on Firm B investing)? A) -$1B) $2C) $7D) $8E) None of the above
Firms A and B are contemplating whether or not to invest in R&D. Each has two options: “Invest” and “Abstain.” A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn’t invent X, it makes $0 in revenue. If a firm invests and is the only one to invent X, it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other’s investment decisions.Which of the following statements are correct? I. If Firm A and Firm B invest, there is a 0.25 probability that Firm A will become a monopolist and make $20 in revenue.II. If Firm A and Firm B invest, there is a 0.25 probability that Firm A…
Firms A and B are contemplating whether or not to invest in R&D. Each has two options: “Invest” and “Abstain.” A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn’t invent X, it makes $0 in revenue. If a firm invests and is the only one to invent X, it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other’s investment decisions. The “research and development” game is best analyzed as a simultaneous move game, because the parties lack information about each other’s investment decisions. Which game (in the attached image)describes the “research and development game”…
Portsmouth Bank has foreclosed on a home mortgage and is selling the house at auction. There are three bidders for the house, Emily, Anna, and Olga. Portsmouth Bank does not know the willingness to pay of these three bidders for the house, but on the basis of its previous experience, the bank believes that each of these bidders has a probability of 1/3 of valuing it at $600,000, a probability of 1/3 of valuing at $500,000, and a probability of 1/3 of valuing it at $200,000. Portsmouth Bank believes that these probabilities are independent among buyers. If Portsmouth Bank sells the house by means of a second- bidder, sealed- bid auction (Vicktey auction), what will be the bank's expected revenue from the sale?
Two partners start a business. Each has two possible strategies, spend full time or secretly take a second job and spend only part time on the business. Any profits that the business makes will be split equally between the two partners, regardless of whether they work full time or part time for the business. If a partner takes a second job, he will earn $20,000 from this job plus his share of profits from the business. If he spends full time on the business, his only source of income is his share of profits from this business. If both partners spend full time on the business, total profits will be $200,000. If one partner spends full time on the business and the other takes a second job, the business profits will be $80,000. If both partners take second job, the total business profits are $20,000. a) This game has no pure strategy Nash equilibria, but has a mixed strategy equilibrium. b) This game has two Nash equilibria, one in which each partner has an income of $100,000 and one in…
Solve the following problem using an excel spreadsheet. A tobacco company isinterested in hiring a salesperson to promote smoking cigarettes in nightclubs. The position pays a flat salary of $50,000, regardless of sales levels. The firm has two applicants, Predictable Patty and Risky Ricky. Predictable Patty can produce with 100% certainty $100,000 a year in sales. Risky Ricky, on the other hand, can produce $300,000 with probability of 50%. But if he turns out to spend his time drinking and dancing in the nightclubs instead of making sales, he could actually cost the firm -$100,000 per year.a) During their first year on the job, what are the expected sales of Patty and Ricky? What are the firm’s expected profits on each worker?b) Now assume both workers are currently 25, and they will work until the retirement age of 65. The firm has the option to fire its new employee after one year based on sales, but can only hire one employee. Assume that it takes only one year to discover whether…
Burger Prince Restaurant is considering the purchase of a $100,000 fire insurance policy. The fire statistics indicate that in a given year the probability of property damage in a fire is as follows: Fire Damage $100,000 $75,000 $50,000 $25,000 $10,000 $0 Probability .006 .002 .004 .003 .005 .980 If Burger Prince was risk neutral, how much would they be willing to pay for fire insurance? If Burger Prince has the utility values given below, approximately how much would they be willing to pay for fire insurance? Loss $100,000 $75,000 $50,000 $25,000 $10,000 $5,000 $0 Utility 0 30 60 85 95 99 100
Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary’s boat wins, Donna would give him $31. If Gary’s boat does not win, Gary would give her $31. Gary’s utility function is p1x^21+p2x^22, where p1 and p2 are the probabilities of events 1 and 2 and where x1 and x2 are his wealth if events 1 and 2 occur respectively. Gary’s total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). Taking the bet would reduce his expected utility. Taking the bet would leave his expected utility unchanged. Taking the bet would increase his expected utility. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. The information given in the problem is self-contradictory.
Consider a medieval Italian merchant who is a risk averse expected utility maximiser. Their wealth will beequal to y if their ship returns safely from Asia loaded with the finest silk. If the ship sinks, their incomewill be y − L. The chance of a safe return is 50%. Now suppose that there are two identical merchants, A and B, who are both risk averse expected utilitymaximisers with utility of income given by u(y) = ln y. The income of each merchant will be 8 if theirown ship returns and 2 if it sinks. As previously, the probability of a safe return is 50% for each ship.However, with probability p ≤ 1/2 both ships will return safely. With the same probability p both willsink. Finally, with the remaining probability, only one ship will return safely.(iv) Compute the increase in the utility of each merchant that they could achieve from pooling theirincomes (as a function of p). How does the benefit of pooling depend on the probability p? Explainintuitively why this is the case.
Obi-Wan is considering whether to buy a lightsaber. With probability 0.50 he will value the lightsaber at $4,000, and with probability 0.50 he will value it at $1,000. If new lightsabers sell for $2,500, then buying a new lightsaber is a: Multiple Choice fair gamble. better-than-fair gamble. less-than-fair gamble. less-than-fair gamble if Obi-Wan risk neutral.
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.
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…