When a consumer searches on Google, related advertisements (so-called sponsored links) appear next to the results. Firms bid for top placement on the page for their links. In a Google ad auction, the firm making the highest sealed bid wins the top position on the Web page and pays a price equal to the second-highest bid. The next highest bidder wins the second position (on the page just below the top position) and pays the third-highest bid, and so on. The price paid for each position is announced to all competing firms.
Suppose that firms 1, 2, 3, and 4 are bidding for two advertising positions. On average, the top page position generates 5 clicks per minute for each firm, while the second position generates only 3 clicks per minute. Based on past experience, each firm estimates the economic value (or net profit) it can expect to earn per click. For firms 1, 2, 3, and 4, these values are 50¢, 35¢, 30¢, and 15¢, respectively.
a. For the firm values listed above, is it an equilibrium for each firm to bid its true value? Or could any of the firms do better by bidding above or below its value? Explain briefly.
b. Alternatively, what if firm 3's value is 20¢ (instead of 30¢)? Is truthful bidding an equilibrium?