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 '01 : 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: '02 : 6 or '02 : 10. Company 1 believes that company 2 has a valuation of '02 : 6 with probability % and a valuation of '02 : 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 rms submit the same bid, then rm 1 wins the auction. A company's payoff is therefore: Vi: {v3- b,- if it wins the auction 0 if it loses the auction Suppose that company 2 bids b2 : 6 when 122 : 6 and bids b2 : 8 when 122 = 10. \\Vhat value of b1 is company 1's best response to this strategy? Hint: explain rst in which cases company 1 wins, then give the probability that these cases occur, and nally compare company 1 's payoff from each possible action it can choose. Suppose that company 1 bids the value of b1 that you found in part 4, [ show that the strategy: 6 if'0226 52W) 2 {8 if '02 = 10 is a best-response for company 2