Macroeconomics and Microeconomics - Auction Theory - Essay Example

?Auction Theory Introduction Auction theory is a study of auction markets and the behavior of both the sellers and buyers in the auction (Calzi, . One of the main characteristics of auctions is the presence of independent and uniformly distributed private valuations, where the bidders in the auction have their own valuations of the items being sold (Kagel and Levin, 2002). In this case, each user attaches a private value to the item being bid on, depending on the relative utility of the item to the user. The independence of the auction depends on each user not knowing the value that the other bidders attach to the item, which means that the bidders will bid independently of each other. The result of the independent valuation of bids is the assumption that each bidder has an intrinsic value for the item which means that the bidder will bid up to this price and not higher than the price (Kagel and Levin, 2002). This true value of the item to each individual bidder gives rise to the rationality of bidders, where they utilize the information they have to make informed bids, and bids not higher than their true or intrinsic value of the auction. As a result of the informational deficiency in the auction, different bidders usually have different bidding strategies. The most common bidding strategies differ according to the type of auction, and as will be discussed in subsequent sections, bidding strategies affect the outcome of the bid. However, the underlying bidding strategy is usually incremental bidding, where the bidder bids until the true value attached to the item is achieved, after which the bidder stops bidding (Kagel and Levin, 2002). Bidding strategies are also linked to the information that the bidder has on the auction. If the true value attached to the item is a value x, and the value of the bid needed by the seller is a higher value y, then the bidder will seek to maximize the surplus from the bid, which can be done by bidding as close to x as possible (David, 2010). Types of Auctions As already stated, there are many different types of auctions; however, these types are usually derived from the four dominant types of auctions (Wellman, Brachman and Dietterich, 2008). The types of auctions are usually dispersed between open and sealed auctions, both of which need different types of bidding strategies (Easley and KleinBerg, 2010). The first type of open auctions is called English or ascending bid auctions, where the auction is usually done in real time. In this case, the seller usually sets a low price as the beginning price, after which the price is increased gradually as the bidder offer their prices. The bidders drop out of the auction as their true values are exceeded until the last bidder gets the item at her intrinsic value. The second type of auction is called Dutch or descending bid auctions, where the seller starts the auction at a high price and then gradually drops until the first bidder states the price and takes the item at the stated price (Easley and KleinBerg, 2010). The main area of focus for this paper is sealed bid auctions, which are divided into two types; first-price sealed bid auctions and second-price sealed bid auctions. The first-price sealed bid auction is one where all the buyers submit simultaneous sealed bids to the seller, who opens them and sells the item to the highest bidder at the stated price (Easley and KleinBerg, 2010). Conversely, second-price sealed bid auctions refer to a case where the buyers submit sealed bids to the seller, who opens them and sells the item to the highest bidder, but at the second highest price. This type of auction is also called Vickrey auctions (Koutsojannis and Sirmakessis, 2009). Informational asymmetry in auctions usually affects the bidding decisions of both the seller and the buyer (Koutsojannis and Sirmakessis, 2009). To describe seller monopoly, consider an auction where the seller attaches a price of x on the item, and the bidder attaches a price of y to the item. In this case, the surplus to the seller and the buyer is the difference between the two prices (Easley and KleinBerg, 2010). If the seller knows the value to which the buyer attaches to the item, then she can announce the price at a value just lower than y, in which case she will get the surplus of the auction. Conversely, if the buyer knows the price to which the seller attaches to the item, then he can state a price just above x, and thus, get the surplus rom the auction. This type of informational asymmetry gives rise to the need for independent, private value auctions, where the buyers know the intrinsic value to which they attach to the item, but they do not know the value attached to the item by the seller or other bidders. Comparison of Sealed Bids to Open Auctions The first comparison is between descending bid auctions and first-price auctions, where we know that, in a descending bid auction, the seller lowers the price until the first bidder gets the item at the highest price (Easley and KleinBerg, 2010). In this case, the bidders keep quiet until the first bidder states the price at which she takes the item in the same case, a first-price sealed bid auction is one where the seller opens the bids and sells the item to the bidder with the highest price. These two types of auctions are similar since the seller will end up selling the item to the highest bidder in the group. Conversely, second-price sealed bid auctions and ascending bid auctions are similar. In this case, we assume that the ascending bid auction goes on until the second highest bidder drops out, in which case, the item is sold to the highest bidder at the price at which the second bidder dropped out (Easley and KleinBerg, 2010). In the same case, the second-price sealed bid auctions is done when the seller opens the bids and sells the item to the bidder with the bidder with the highest bid, but at the price of the second highest bidder. First-price Sealed Bid Auctions As already stated, the main focus of this paper is sealed bid auctions and their dominant strategies. In the case of first-price sealed bid auctions, the value of the bid affects both the winning fact and how much the winning bidder pays for the item (Ma and Leung, 2008). The game theory setting for this kind of bid is to set up the bidders as players, where a bidder i assigns a value v to the item and bids at a price b. The derivation of the payoff strategy indicates that, if b is not the winning bid, then the payoff to the bidder i is 0, but if the bid placed by the bidder is a winning bid, then the payoff that the bidder gets is the difference between v and b. Looking at the above bidding strategy, it is evident that bidding the true value is not a dominant strategy, since the bidder would get a payoff of 0 irrespective of whether the bid is a winning or losing bid (Courcoubetis & Weber, 2003). To explain this, consider the above scenario; if the bidder loses, the payoff is 0, and if the bidder wins, the difference between the bid b, and the true value v, is still 0. Therefore, the optimal strategy in this case is to shade the bid, or to bid at a price slightly lower than the true value that the bidder attaches to the item, which ensures that the payoff is substantial (Ma and Leung, 2008). However, the shading of the price should be done rationally, since shading too close to the true value will give a small payoff, and shading too far below the true value might provide a losing bid. The shading is done by considering the two opposing forces, bidding too close to the true value gives an irrelevant payoff, and bidding too low might result in a bid lower than the highest bid, which increases the chances of losing the auction. Second-Price Sealed Bid Auctions Second-price sealed auctions also have a dominant strategy, where the bidder is advised to bid at the true value of the item. The dominant strategy in this type of auction is bidding at the price at which the item is worth to the bidder. To set up this strategy as a game theory, consider the bidder i’s true value as v, the bid as b, and the second highest bid as b1 (Thomas, 2003). In this case, it is evident that, if b is not the wining bid, then the payoff to bidder i is 0, and if the bid b is the winning bid, then the payoff is equal to v- b1. The dominant strategy in the case of second-price sealed bids is a truthful strategy, where the bidder bids the price of her true value as assigned to the item, since deviations from the price does not increase the payoff earned (Talluri and Ryzin, 2005). Conclusion This paper focused on first-price and second-price sealed auctions. After the analysis, it is evident that the strategies for both types of auctions vary, since first-price sealed bid auctions are dominated by the strategy of shading the price, or bidding at a price lower than the true value assigned to the item. Conversely, the dominant strategy for second-price sealed bid auctions is to bid at a price equal to the true value assigned to the item. This paper has also determined that first-price sealed bid auctions are similar to descending bios, while second-price sealed bid auctions are similar to ascending bids. References Calzi, M. L. 2010. Progress in Artificial Economics, A Computational And Agent-Based Models, New York, Springer. Courcoubetis, C. & Weber, R. 2003. Pricing Communication Networks: Economics, Technology and Modeling, New York. John Wiley & Sons. David, E. 2010. Agent –Mediated Electronic Commerce. Designing Trading Strategies and Mechanisms for Electronic Markets, New York, Springer. Easley, D, and KleinBerg, J, 2010. Networks, Crowds, and Markets: Reasoning about a Highly Connected World, Cambridge, Cambridge University Press. Kagel J. H. & Levin D. 2002. Common Value Auctions and the Winners Curse, Brussels, Princeton University Press. Koutsojannis, C. & Sirmakessis, S. 2009. Tools and Applications with Artificial Intelligence, New York: Springer. Ma, H. & Leung, H. 2008. Bidding Strategies in Agent-Based Continuous Double Actions, New York, Springer. Talluri, K.T. & Ryzin, G. V. 2005. The Theory and Practice of Revenue Management, New York, Springer. Thomas, L. C. 2003. Games, Theory and Applications, London, Courier Dover Publications. Wellman, M., Brachman, R. & Dietterich, T. 2008. Trading Agents, California, Morgan & Claypool Publishers. Read More