The expected payoff to Internet auctions

In an Internet auction, the expected payoff acts as a benchmark of the reasonableness of the price that is paid for the purchased item. Since the number of potential bidders is not observable, the expected payoff is difficult to estimate accurately. We approach this problem by considering the bids as a record and 2-record sequence of the potential bidder's valuation and using the Extreme Value Theory models to model the tail distribution of the bidder's valuation and study the expected payoff. Along the discussions for three different cases regarding the extreme value index gamma, we show that the observed payoff does not act as an accurate estimation of the expected payoff in all the cases except a subclass of the case gamma = 0. Within this subclass and under a second order condition, the observed payoff consistently converges to the expected payoff and the corresponding asymptotic normality holds.