Elementos de análisis particulares de las cinco escuelas estudiadas

In conclusion, this chapter presents a new model of sequential auctions, where bidders enter bidding at different auctions, and their lifespans overlap. The model is used to show that such a case has implications for learning by the bidders. Previous prices are a source of information about the expected distribution of bidders valuations, as in the standard sequential auctions model, and additionally they carry information about the expected composition of bidders with different horizon lengths in future periods. It is shown that from the point of view of an external observer, the informativeness relating to bidders valuations lasts only until the last bidders present in the period of information acquisition exit. On the other hand, learning relating to the composition of young and old bidders extends over all the future periods. An introduction of one bidder with a 3-period lifespan, who is able to observe a price after their first bid, into the equilibrium environment of overlapping generations model with 2-period bidders makes the bidder update their expectation of composition of young and old bidders int+ 1 (the last period of the 3-period bidder), even though none of the other bidders from t −1 (the period of price observation) are present in t+ 1. Based on that, the 3-period bidder updates their bid in their middle period, expecting a different composition of young and old 2-

period lived bidders int+ 1. This is a novel result, in comparison to the standard model of sequential auctions, where the only channel for learning is through updating on the expected valuations of bidders in future periods. Unlike in the standard model, it is not a necessary condition that the same bidders should be present in the period of information acquisition and the period for which learning is applied.

Chapter 2

Empirical investigation based on

sequential auctions theory

2.1

Introduction

The current chapter is the analysis of auction data with respect to the sequential auc- tions theory outlined previously. Two main hypotheses are tested. First of all the data is analyzed with respect to the expectation of bid discounting by bidders of younger gen- erations. The theory predicts that bidders should be increasing their bid in sequential auctions, by reducing discounting of their valuation of the product. Forward-looking bid- ders that plan to bid in future auctions should take that into account in their bidding strategy. Secondly, the overlapping generations model predicts correlation between price in previous auction on bidding in the following auction. Higher prices in previous auc- tions have an effect on beliefs about the competition present in the following auctions one step further to the future, which induce bidders to increase their bids. Literature search revealed no existing studies testing those predictions. Previous empirical tests of sequential auctions usually focused on a dissonance between theoretical prediction about increasing prices and empirical observations. The empirical analyses found in literature were focused mostly on price patterns in sequential auctions, while the current chapter is trying to answer questions about bidding strategies and its links to previous prices. The model of sequential auctions considered predicts linkage between observation of past prices and bidding strategy. It is expected that an effect of prices on bidding in the following auctions is monotonous. Online auction marketplaces for consumer goods are a good place to test the predictions of the OLG model because of participation of many bidders and a tendency among them to take part in more than one auction for the same product. On the other hand, bidders sometimes place bids in parallel auctions, and there- fore, in order to identify the impact of learning from past prices, one has to ensure that sequentiality is satisfied.

2.2

Literature

The most influential empirical paper discussing the theory of sequential auctions was the investigation of wine auctions in Ashenfelter(1983)[3].The authors found that the price in sequential auctions was declining, in contrast to predictions of the earlier theory - increasing price. The declining price was explained by risk-aversion in McAfee and Vin- cent (1993) [25], and by the deviation from Perfect Equilibrium strategy, as discussed in Milgrom and Weber (2000)[27], but also by the fact that high-valuation bidders win at the beginning, which creates a declining distribution of bidders left in later auctions. Until the boom in popularity of online auctions the availability of data on sequential auctions of identical objects was limited. Empirical investigation of price in sequences of auctions has given the researchers the grounds to add modifications to the theory of Common Values component and risk-aversion, as well as deviations from the PBE strat- egy. Interestingly, the empirical studies have focused on investigation of only the price in the auctions, while the most fundamental prediction of sequential auctions theory - that bidders increase their bid in following auctions has not been tested, possibly due to the lack of availability of data for individual bidders. In my investigation I am looking at strategies of individuals in the sequence of second price auctions. The main predic- tion of the theory presented herein is the increase of bids in sequential auctions. The empirical results confirming that are obtained using the advantage of individual-bidder data. The increases of bids is a common component in all versions of private values sequential auctions models - not depending on the horizon, number of future auctions or risk-aversion. The fundamental question addressed is whether Game Theory provides us with good predictions for the individual strategies in sequential auctions. The addition of overlapping generations of buyers to the model does not change the prediction about bid increases. Another prediction of the model tested is the influence of past prices on bidding in the next auction, which, if found to be present, would confirm the hypothesis that bidders learn by observation of results of previous auctions.

eBay auctions have been studied before, whereby most of the literature about buyer’s behavior is focused on the investigation of features which deviate from basic theoretical model, such as bidding multiple times during one auction or last minute bidding. A summary of literature dealing with eBay can be found in the review paper by Hasker and Sickles (2010)[18]. As authors summarize, there are several main tactics of buyers, which include: Sniping (Last Second Bidding), Incremental Bidding, and Squatting (large early bids) or Jumping. The availability of proxy bidding enables the bidder to enter the highest price they are willing to pay for the item, allowing them to save time incurred to increase their bid later.However, this strategy is not always used and in many cases multiple bidding occurs.

Despite these additional aspects of behavior at online auctions, the theory about sequen- tial auctions is still relevant when looking at final bids of bidders in each auction. Put aside multiple bidding and the timing of the bid placement, the final bids should be representative of bidder’s valuation for the auctioned item. Ability to observe how indi- vidual bidders bid in a sequence of online auctions and availability of such data provides an opportunity to test the fundamental theory of sequential auctions. The addition of overlapping generations, as introduced in this thesis, is relevant to this data, since the generations of bidders are seen to clearly overlap in the studied auction setting.

Online auctions data typically contain anonymized user names. Literature search have not shown previous attempts at dealing with this problem, and the method presented herein could be shown to be of benefit in future research in this field.