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Creating a loyal customer base is one of the most important, and at the sametime, most difficult tasks a company faces. Creating loyalty online (e-loyalty)is especially difficult since customers can ``switch'' to a competitor with theclick of a mouse. In this paper we investigate e-loyalty in online auctions.Using a unique data set of over 30,000 auctions from one of the mainconsumer-to-consumer online auction houses, we propose a novel measure ofe-loyalty via the associated network of transactions between bidders andsellers. Using a bipartite network of bidder and seller nodes, two nodes arelinked when a bidder purchases from a seller and the number of repeat-purchasesdetermines the strength of that link. We employ ideas from functional principalcomponent analysis to derive, from this network, the loyalty distribution whichmeasures the perceived loyalty of every individual seller, and associatedloyalty scores which summarize this distribution in a parsimonious way. We theninvestigate the effect of loyalty on the outcome of an auction. In doing so, weare confronted with several statistical challenges in that standard statisticalmodels lead to a misrepresentation of the data and a violation of the modelassumptions. The reason is that loyalty networks result in an extremeclustering of the data, with few high-volume sellers accounting for most of theindividual transactions. We investigate several remedies to the clusteringproblem and conclude that loyalty networks consist of very distinct segmentsthat can best be understood individually.

E-loyalty networks in online auctions