Prospect theory in auctions

We apply prospect theory to independent private value auctions by the seller who auctions off an item. Kahneman and Tversky (1979) introduced prospect theory where they used a value function in place of a utility function and used a weighting function in place of a probability function. We introduce a new behavioral factor into auction theory. Based on interviews with 180 students, we found there were two types who interpreted the fact of winning an auction against m other bidders differently. The first type recognized 2m different outcomes, each of which corresponded to whether s/he won or lost against one of his m rival bidders. Therefore, winning the auction was characterized by the fact that m winning outcomes happened simultaneously to her/him. In contrast, the second type distinguished only two outcomes, whether he/she won an auction, or lost. Among 180 students, 11% was the first type and 89% was the second type. We characterize the equilibrium bidding functions of sealed-bid first-price auctions and those of sealed-bid second-price auctions when all the bidders are type one, or type two. While bidding her/his true value is still a dominant strategy in a sealed-bid secondprice auction, both type one and type two bidders shade his/her bid more than an expected utility maximizing bidder when his/her value is relatively low and bids higher than an expected utility maximizing bidder when his/her value is very high. We use simulation methods to explicitly compare the expected revenue of the seller among different auction procedures. We parameterize a weighting function and use uniform distributions for bidders’ valuations for this purpose. The expected revenue of the seller is highest for a sealed-bid first-price auction with type two bidders, is lowest for a sealed -bid first-price auction with type one bidders, and the expected revenue of a sealed-bid second-price auctions regardless of bidders’ types is in the middle. For expected utility maximizing bidders, Myerson’s revenue equivalence theorem implies any efficient auction including sealed-bid first-price and second-price auctions induces the same revenue as that in a sealed-bid second-price auction in our model because truth-bidding is still the equilibrium in a sealed-bid second-price in our model. Although our interviews with students showed that there were two types of bidders, our model assumed every bidder has the same type. Extending our analysis to two types coexisting model is our future task.