The theory of auction has become an active research area spanning multiple disciplines such as economics, finance, marketing and management science. But a close examination of it reveals that most of the existing studies deal with ascending (i.e., English) auctions in which it is assumed that the bid increments are continuous. There is a clear lack of research on optimal descending (i.e., Dutch) auction design with discrete bid levels. This dissertation aims to fill this void by considering single-unit, open-bid, first price Dutch auctions in which the bid levels are restricted to a finite set of values, the number of bidders may be certain or uncertain, and a secret reserve price may be present or absent. These types of auctions are most attractive for selling products that are perishable (e.g., flowers) or whose value decreases with time (e.g., air flight seats and concert tickets) (Carare and Rothkopf, 2005). I began by conducting a comprehensive survey of the current literature to identify the key dimensions of an auction model. I then zeroed in on the particular combination of parameters that characterize the Dutch auctions of interest. As a significant departure from the traditional methods employed by applied economists and game theorists, a novel approach is taken by formulating the auctioning problem as a constrained mathematical program and applying standard nonlinear optimization techniques to solve it. In each of the basic Dutch auction model and its two extensions, interesting properties possessed by the optimal bid levels and the auctioneer's maximum expected revenue are uncovered. Numerical examples are provided to illustrate the major propositions where appropriate. The superiority of the optimal strategy recommended in this study over two commonly-used heuristic procedures for setting bid levels is also demonstrated both theoretically and empirically. Finally, economic as well as managerial implications of the findings reported in this dissertation research are discussed.

Detta är en undersökning som är gjord för att jämföra prissättningen av fastigheter som är till salu i Sverige och Spanien. För att avgränsa oss har vi valt att jämföra Stockholms innerstads prissättning med prissättningen i Palma på Mallorca i Spanien. Lockpris fenomenet har fått hård kritik under den senaste tiden i media. På grund av denna kritik så har många mäklare, speciellt i Stockholms innerstad, gått ihop och arbetar mot att undvika lockpriser och har infört begreppet accepterat pris. Dock kan accepterat pris uppfattas som ett nytt ersättningsnamn på lockpriser. Trots att Mäklarsamfundet tar bestämt avstånd från användning av lockpriser så har vi genom intervjuer med mäklare i Stockholms innerstad fått fram att detta används fortfarande vid prissättning av bostäder. Vi har genom våra intervjuer med fastighetsägare i Stockholm och Palma, mött flera fastighetsägare som har känt sig lurade då de har köpt en fastighet till ett avsevärt mycket högre slutpris än utgångspris. Samtidigt har vi mött flera fastighetsägare som är nöjda med Sveriges budgivningssystem. De flesta föredrar dock att köpa eller sälja en fastighet till verkligt accepterat pris. Det spanska budgivningssystemet där budgivningen går nedåt har, trots att de flesta fastighetsköpare som vi intervjuat lyckats förhandla ned slutpriset, mötts med en del kritik. Största delen av kritiken bygger på att priset inte sätts relaterat till marknadspriset, vilket det trots lockpriser, görs i Sverige. / This is a survey where we compare the pricing of properties that are for sale in Sweden and Spain. To make delimitation, we have chosen to compare the pricing in the inner city of Stockholm of Sweden with the pricing in Palma in Mallorca, Spain. The cap rates phenomenon has been very criticized in the Swedish media in the latest couple of years. Because of this criticism, many real estate agents in the inner city of Stockholm are working to avoid cap rates and introduced the concept of using acceptable prices. However, acceptable price rates are perceived as a replacement name for the cap prices. Although the Mäklarsamfundet, of Sweden, disagrees with the use of cap rates, we have trough our interviews with real estate agents in the inner city of Stockholm received that this concept is still used in the pricing of properties. We have, through our interviews with property owners in Stockholm and Palma, met several property owners who have felt cheated when they bought a property at a significantly higher final price than the asking price. We have as well met several property owners who are satisfied with the Swedish pricing. But most people prefer to buy or sell a property at fair agreed price, using acceptable pricing. Many of the Spanish property buyers who we have interviewed are critical to the Spanish pricing, where the bidding goes down. This despite that most of them, managed to negotiate down the final price. Most of the criticism is based on that the prices are not related to market price, which, despite the cap rates, is in Sweden.

Many people still confused and misunderstand the differences between auction types: In fact, we have only two major types of auctions which are the forward auction and Reverse auction[22]. In a forward auction a single seller offers an item for sale with many competitive buyers driving the price upward: In a Reverse Auction, a single buyer wants to purchase a service or an item from many sellers, they drive the price downward: There are many differences between these type of auction: Including the progress of the auctions; winner selection criterion and other factors: The Reverse Auction nowadays is one of the most preferred types of online auctions: It gains popularity rapidly because of representing the buyers' side and helps him to drive prices down in contrary with the forward auction or traditional auction. The aim of this study is to identify the most common types of the Reverse auctions and compare them to one another to determine when should be used by a buyer and propose the most efficient implementation model for some types: The results of this study are: achieve a written report and a small demonstrator model on how to implement English Auction and Second-Sealed bid Auction.