Firm Z is one of the 5 bidders, each with a value independently drawn from the range $100,000 to $160,000 with all values in between being equally likely. In a sealed-bid auction, Firm Z's equilibrium bidding strategy is: A) b_i = (.2)(160,000) + .8v_i B) b_i = (.5)(160,000) + .5v_i C) b_i = (.25)(100,000) + .75v_i D) b_i = (.2)(100,000) + .8v_i E) b_i = (.8)(100,000) + .2v_i

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To find the equilibrium bidding strategy of Firm Z, we need to use the principle of expected value. Let's say that Firm Z's bid is b and the highest bid among the other 4 bidders is v. Then, Firm Z will win the auction if b>v and lose if b<=v. The probability that Firm Z's bid is the highest among all 5 bids is 1/5. Therefore, the expected payoff for Firm Z if it bids b is: $$E( ext{Payoff}) = P( ext{Win})(b-v)+P( ext{Lose})(0) = \frac{1}{5}(b-v)$$ To find the bidding strategy that maximizes expected payoff, we need to differentiate the expected payoff with respect to b and set it to zero: $$\frac{dE( ext{Payoff})}{db} = \frac{1}{5}= 0$$ This implies that: $$b = v$$ In other words, Firm Z's optimal bidding strategy is to bid its true value. The expected payoff in this case is: $$E( ext{Payoff}) = \frac{1}{5}(v-v) = 0$$ Therefore, Firm Z should bid: $$b_i = (.2)(100,000) + .8v_i$$ which is equivalent to choosing answer choice D.

Firm Z Is One of the 5 Bidders, Each with a Value