Consider two companies bidding to be at the top of a search engine's results for a given keyword. Company 1 values the top position at v₁ = 8. Both company 1 and company 2 know company 1's value. However, only company 2 knows its own valuation for the top position, which can take two values: v2 = 6 or v₂ = 10. Company 1 believes that company 2 has a valuation of 2 = 6 with probability and a valuation of v2 = 10 with probability. Each company chooses simultaneously whether to submit a bid of b = 6 or a bid of b= 8. The company which submitted the highest bid wins the auction and obtains the top position in the search engine. If both firms submit the same bid, then firm 1 wins the auction. A company's payoff is therefore: V₁ = [v₁ - bį if it wins the auction To if it loses the auction 1) Suppose that company 2 bids b2 = 6 when v2 = 6 and bids b2 = 8 when v2 = 10. What value of b1 is company 1's best response to this strategy? Hint: explain first in which cases company 1 wins, then give the probability that these cases occur, and finally compare company 1's payoff from each possible action it can choose.

Consider two companies bidding to be at the top of a search engine's results for a given keyword. Company 1 values the top position at v₁ = 8. Both company 1 and company 2 know company 1's value. However, only company 2 knows its own valuation for the top position, which can take two values: v2 = 6 or v₂ = 10. Company 1 believes that company 2 has a valuation of 2 = 6 with probability and a valuation of v2 = 10 with probability. Each company chooses simultaneously whether to submit a bid of b = 6 or a bid of b= 8. The company which submitted the highest bid wins the auction and obtains the top position in the search engine. If both firms submit the same bid, then firm 1 wins the auction. A company's payoff is therefore: V₁ = [v₁ - bį if it wins the auction To if it loses the auction 1) Suppose that company 2 bids b2 = 6 when v2 = 6 and bids b2 = 8 when v2 = 10. What value of b1 is company 1's best response to this strategy? Hint: explain first in which cases company 1 wins, then give the probability that these cases occur, and finally compare company 1's payoff from each possible action it can choose.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.7P

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Consider two companies bidding to be at the top of a search engine's results for a given keyword. Company 1 values the top position at v₁ = 8. Both company 1 and company 2 know company 1's value. However, only company 2 knows its own valuation for the top position, which can take two values: v₂ = 6 or v₂ = 10. Company 1 believes that company 2 has a valuation of v2 = 6 with probability and a valuation of v2 = 10 with probability. Each company chooses simultaneously whether to submit a bid of b = 6 or a bid of b = 8. The company which submitted the highest bid wins the auction and obtains the top position in the search engine. If both firms submit the same bid, then firm 1 wins the auction. A company's payoff is therefore: V₁₂ = -{- Vi - bi if it wins the auction if it loses the auction 1) What are the possible types of company 2?
Consider two companies bidding to be at the top of a search engine's results for a given keyword. Company 1 values the top position at v₁ = 8. Both company 1 and company 2 know company 1's value. However, only company 2 knows its own valuation for the top position, which can take two values: v₂ = 6 or v2 = 10. Company 1 believes that company 2 has a valuation of v₂ = 6 with probability and a valuation of v₂ = 10 with probability. Each company chooses simultaneously whether to submit a bid of b = 6 or a bid of b = 8. The company which submitted the highest bid wins the auction and obtains the top position in the search engine. If both firms submit the same bid, then firm 1 wins the auction. A company's payoff is therefore: Vi = 0 bi if it wins the auction if it loses the auction 1) Discuss what other aspects of advertising on Google which are not captured by the model might be relevant in a real situation.
Question 2. In an industry, there is an incumbent firm (Firm 1) and there is a potential entrant firm (Firm 2). Firm 1 decides whether to build a new plant, and simultaneously Firm 2 decides whether to enter into this industry. The cost of building a new plant for Firm 1 can be high or low, which is Firm 1's private information. Firm 2 is uncertain about Firm 1's cost, and believes that with probability TE [0, 1] the building cost for Firm 1 is high, and low with probability 1-7. The payoffs are depicted below. Build Not Build Enter 0, -1 2,1 Not Enter 2,0 3,0 High Cost Build Not Build 1 Enter 1.5, -1 2,1 Not Enter 3.5,0 3,0 Low Cost This interaction comprise a Bayesian game. Firm 2 does not know the matrix in which they are in, but Firm 1 does now it. As we have seen in class, there are 5 things that define this Bayesian game. 1. Set of players: N {Firm 1, Firm 2}. = 2. Set of actions for each player: A₁ = {Build, Not Build}, A2 3. Type space of Firm 1: ₁ = {H, L}. {Enter, Not Enter}.…
"Jay, a writer of novels, just has completed a new thriller novel. A movie company and a TV network both want exclusive rights to market his new title. If he signs with the network, he will receive a single lump sum of $1,480,000, but if he signs with the movie company, the amount he will receive depends on how successful the movie is at the box office.The probability of a small box office earning $203,000 is 0.27. The probability of a medium box office of $1,660,000 is 0.49, and the probability of a large box office of $2,950,000 is 0.24.Jay can send his novel to a prominent movie critic to assess the potential box office success. It will cost $20,000 to get the novel evaluated by the movie critic.The movie critic can have either a favorable or unfavorable opinion. The movie critic's reliability of predicting box office success is as follows.If the movie will have a large box office, there is a 0.75 probability the critic will have a favorable opinion.If the movie will have a medium…
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Consider an investor with initial wealth yo, who maximizes his expected utility from final wealth, E[u()]. This investor can invest in two a risky securities, 1 and 2, with random return ři and ř2. Those risky returns are two binomial variables, perfectly correlated. More specifically, with probability p we have ř =r and r, = r+ô, and with probability 1- p we have î = 0 and ř2 = -6, where r> 0 and ổ > 0. We assume that this investor has log preferences, that is u(y) = log(y). 1. For a given fraction, a, of the initial wealth, invested in risky security 2, what is the distribution of final wealth, g1? 2. Determine the expression of Elu(1)] as a function of a. 3. Explain why there is an upper bound and a lower bound for a, and determine those bounds. 4. Determine the optimal fraction a*. 5. When p = 0.5, describe qualitatively the optimal investment strategy. Does it make sense?
FINITE REPETITION Alice and Bob are playing a repeated game in which a certain stage game is played twice in succession. All behaviour in the first period is observed by both players before the second period commences. In the stage game, Alice has 2 pure strategies and Bob has 3 pure strategies. How many pure strategies does Bob have in the repeated game? (If necessary, use a calculator to compute this number.) 6. 36 216 128 64 3 729 2187
You are one of five risk-neutral bidders participating in an independent private values auction. Each bidder perceives that bidders' valuations for the item are evenly distributed between $20,000 and $50,000. For each of the following auction t determine your optimal bidding strategy if you value the item at $35,000. a. First-price, sealed-bid auction. O Bid $20,00. O Bid $50,00. O Bid $35,00. O Bid $32,000 b. Dutch auction O Let the auctioneer continue to lower the price until it reaches $20,000, and then yell "Minel". O Let the auctioneer continue to lower the price until it reaches $35.000, and then yell "Mine!" O Let the auctioneer continue to lower the price until it reaches $32,000, and then yell "Mine!" O Let the auctioneer continue to lower the price until it reaches $50,000, and then yell "Mine!". C. ond-price, sealed-bid auction O Bid $50,00. O Bid $35.000 O Bid $32,00. b. Dutch auction. O Let the auctioneer continue to lower the price until it reaches $20,000, and then yell…
FINITE REPETITION Alice and Bob are playing a repeated game in which a certain stage game is played twice in succession. All behaviour in the first period is observed by both players before the second period commences. In the stage game, Alice has 3 pure strategies and Bob has 2 pure strategies. How many pure strategies does Bob have in the repeated game? (If necessary, use a calculator to compute this number.) 2 6 2187 3 36 64 7 729 128 216 Please do fast ASAP fast
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…
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?
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.