Introduction 

It is quite conceivable that the inclusion of large numbers of software agents as economic players will have a strong effect upon the global economy, giving rise to collective phenomena that are rare or even unknown in today's economy. We believe this because software agents differ from human agents in a number of economically relevant ways. They are capable of making decisions orders of magnitude faster than humans, and can potentially base those decisions on greater volumes of much fresher information. Within limited domains, they can in some cases be more capable than humans. In general, however, they are considerably less intelligent and flexible. Our previous work on an economy of information-filtering agents has shown that these differences, coupled with the reduced friction that one expects to find in agent-based information economies, can engender rampant price wars in which sellers' prices undergo periodic oscillations that can be harmful to sellers and buyers alike [1, 2, 3].

Another important distinguishing feature of software economic agents is that they are fundamentally more consistent and understandable in their individual behavior than their human counterparts. Understanding and modeling the decision-making behavior of individual humans is notoriously difficult. Mathematical utility functions are often used to model human choices, but this can only be taken to be a rough approximation. In contrast, the behavior of a software agent is codified completely in the form of a computer program. Thus, models of software agents can be regarded as proposals for, rather than just approximate descriptions of, the behavior of boundedly rational individuals. This permits a different research emphasis. Rather than measuring our success in terms of our ability to understand individual and societal behavior, our goal is to design an agent economy that will work well from the perspective of the individual agents that participate in it. Our study of the collective dynamics of large number of economic software agents [1, 2, 3, 4] is not an end in itself; it is motivated by the hope that we can derive principles that will help us to design effective agent strategies, interaction protocols, and market mechanisms [5].

The information-filtering economy that we have studied previously is an example of a horizontally differentiated [6] market: an article that is worthless to one consumer may be priceless to another. However, in a broad information economy of the sort we envision, there will also be a number of markets in which information goods and services are vertically differentiated, i.e. there is near-universal agreement among consumers of what constitutes higher or lower quality.

For example, a population of human or software-agent consumers of network services will have diverse requirements, and network providers will jockey for position in the market by offering a variety of tradeoffs between price and quality of service (QoS). Note that, in general, quality may be a multi-dimensional concept [6, 7, 8]. An agent representing a multimedia application might require a transmission rate of between 1.5 Mbps and 3.0 Mbps in order to support compressed real-time video (MPEG-II or JPEG). Additionally, it might require a maximum packet-loss probability of 1% and a maximum packet delay of 20 msec in order to support a minimum guaranteed viewing quality. Suppose that a given provider can meet these basic requirements for a certain fee. The multimedia agent might still prefer to patronize a higher-priced supplier that offers a higher transmission rate, a lower packet-loss probability, or a smaller packet delay. The degree to which it is willing to pay for extra quality in any of these three dimensions depends on how that extra quality will translate into improvements in the quality of the service that the multimedia agent can offer to its customers, and how much more it could charge for this improved service. As the demands placed on the multimedia agent may vary from one moment to the next, so in turn will the demands that it makes upon the network service providers. A network services market will be expected to offer multiple services at multiple rates, with low costs and latencies for switching from one service type to another. Market mechanisms capable of supporting these requirements are a topic of active research [9, 10].

As a second example, consider a market in which information brokers compete to provide information filtering services. As has been discussed, the varied preferences among users for different categories of information induce horizontal differentiation. However, there may be several vertical dimensions as well. Different brokers could offer different response times. One broker could, by using a faster processor or a more clever algorithm, implement a more sophisticated and accurate filtering algorithm than another.

Numerous works in the economics literature treat various aspects of the behavior of horizontally and vertically differentiated markets [6, 8, 11, 12, 13, 14, 15]. This paper differs from these previous works in that it presents a comparative study of non-equilibrium price dynamics resulting from a wide range of different individual pricing strategies that might be employed by software agents, and differs from our own previous work in that it considers a vertically- rather than a horizontally-differentated market. We are particularly interested in determining whether vertically differentiated markets are vulnerable to the same pathological, cyclical price wars that we have observed previously in a horizontally differentiated market in which seller agents offer filtered streams of news articles to buyer agents [1, 3].

After presenting the model in section 2, we shall find in sections 3 and 4 that, under some circumstances, the model does exhibit cyclical price wars. In section 5, we discuss the mechanisms that underlie these dynamics, and conclude that, just as in our previous work, much can be attributed to the topology of the sellers' profit landscapes. Finally, we summarize our findings and point out directions for future work in section 6.