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.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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