The economic model developed in this paper was designed to investigate the potential impact of increasing numbers of on-line shopbots on markets. To this end, our model allows for the co-existence within a single market of a variety of strategies by which buyers choose sellers -- some buyers use shopbots to find the lowest-priced sellers of desired goods, while other buyers do not -- and a variety of strategies by which sellers dynamically set their prices for goods and services. Initially, we obtained results on the nature of equilibrium, assuming sellers behave according to the dictates of game theory. In particular, analysis revealed a unique Nash equilibrium in which all but one of the sellers set their price to the monopolistic price. The remaining seller chooses a lower price, the exact value of which decreases monotonically towards the production cost as the fraction of buyers employing shopbots increases, and as competition (i.e., the number of sellers) increases. Overall, we observe that the presence of shopbots in the marketplace drives equilibrium prices down.
Upon having computed the game-theoretic equilibrium, our focus shifted to the study of whether adaptive learning yields the derived solution. We considered several alternative pricing strategies which sellers might implement, some of which require the sort of pricing information that is provided by shopbots. We observed a variety of collective modes of behavior. Price wars occur when all sellers utilize the myoptimal pricing strategy; this behavior can be attributed to the multi-peaked nature of the underlying profit landscape. Price wars, however, are not an unmitigated disaster from the sellers' viewpoints, since each seller receives higher average profits than it obtains at the Nash equilibrium.
Surprisingly, when all sellers use a simple derivative-following algorithm -- making no use of knowledge regarding other sellers or the buyers -- they evolve towards a collusive state in which all sellers charge the monopolistic price. Consequently, the individual sellers earn much larger profits than are obtained in societies of pure game-theoretic or myoptimal sellers. This presents an interesting social dilemma, however: if any one of the derivative followers were to defect by choosing a more sophisticated strategy, it could easily exploit the remaining derivative followers, earning greater profits for itself, but reducing the total profits received by the seller population.
In this paper, we also considered the interplay of agents who employ different price-setting algorithms. We found, for example, that myoptimal sellers outsmart derivative followers. It is possible, however, that given the choice, sellers might opt for the opportunity to act as a derivative follower for a while, so as to lure others towards cooperative behavior, and then once trusted, defect to myoptimal price-setting. More sophisticated learning algorithms of this nature, which allow sellers to experiment with mixtures of various price-setting strategies, are described in the Appendix of [7]. The adaptation of these algorithms to the study of shopbot economics will be the subject of future research.
Finally, we noted that in the presence of shopbots who efficiently convey pricing data from buyers to sellers, there is an incentive for sellers to reset their prices at ever-faster rates, potentially leading to an arms race, that, in the absence of any intervening mechanism, threatens to choke the Internet with requests for pricing information. In future work, we intend to investigate the design of shopbots who charge for the information they provide (rather than or in addition to subjecting human patrons to advertisements), as a natural way in which to ameliorate the problem of overuse that is likely to arise in the context of information economies and related network interactions. (For more details on pricing as a means of controlling network traffic, see, for example, [5, 20].)
As presented here, our model omits a number of effects that are likely to be essential to understanding the overall impact of shopbots. For example, a natural way to avoid price wars and arms races is to distinguish one's products from others via quality differentiation, such that products cannot be compared according to price alone. Already, most shopbots report on other product attributes, in addition to price; for example www.acses.com reports each book's estimated delivery time. Previous work [9, 11] suggests that this may have the analogous effect of increasing competition in the quality space, just as shopbots that convey pricing data are destined to foster price competition. We intend to extend our model to accomodate quality attributes in order to verify this conjecture. This tendency towards more realistic economic modeling should help us to gain an understanding of the true value of efficient and reliable price and quality information to both buyers and sellers.