Optimal Reserve Price In Sealed Auction With Loss-averse Buyers

Auction is an ancient and effective mechanism for price discovery and resource allocation.With thousands of years' development,various formats of auctions have been created,such as British auction,Dutch auction and sealed-bid auctions.Although auction has been widely used in practice for a long history,academic research on auction just began nearly half a century ago,marked by the pioneering work done by Vickrey(1961).Within symmetric independent private value(SIPV)model,many scholars conduct further studies and contribute significant findings in the auction theory,including the design of auction mechanism,buyers' bidding strategies and sellers' optimal reserve price.In this research,the reference effect and loss aversion are incorporated into the buyer's utility in the symmetric independent private value models of sealed-bid auctions.The buyer's bidding strategy in equilibrium and the seller's optimal reserve price are derived in the first-price and second-price sealed-bid auctions.In both auctions,the seller's expected revenue function is quasi-concave in the reserve price and thus the optimal reserve price is unique.The seller's optimal reserve price and expected revenue increase with the reference point.Furthermore,a comparison of the reserve prices as well as the seller's revenues under the two auctions are conducted.The results show that the seller sets a higher optimal reserve price but obtains a lower optimal expected revenue in the second-price sealed-bid auction than in the first-price sealed-bid auction.In other words,the well-known revenue equivalence principle is no more valid in this case.Specifically,the introduction of lossaversion increases the penalty of paying more than the reference point.Due to loss aversion,the winner obtains a lower expected utility in the second-price sealed-bid auction than in the first-price sealed-bid auction.As a result,a buyer tends to bid more conservatively and hence the seller obtains a lower expected revenue in the second-price sealed-bid auction than in the first-price sealed-bid auction.When determining the reserve price,the seller needs to balance the probability of a successful auction and the selling price of the item.A higher reserve price means a higher selling price and a lower success probability.The loss aversion changes the bidding strategies of the buyers in both auction mechanisms.However,it exhibits more significant influence on buyers' bidding behavior in the second-price sealed-bid auction.Consequently,instead of setting a low reserve price to induce more buyers to participate,it is more beneficial for the seller to set a high reserve price so as to raise the selling price in the case of a successful auction.