Conclusion

Cyclical price wars are an undesirable but fundamental mode of collective behavior in our model economy of information filtering agents that optimize (or nearly optimize) their short-term utility. When the agents are permitted to simultaneously optimize both their price and their product (i.e. the categories they offer to consumers), a more complex cycle in price/product space is typically observed. The natural tendency of agent economies to self-organize into non-competitive niches [Hanson and Kephart, 1998] is thwarted, and agents tend to compete for the same (possibly narrow) market, leaving consumer demand in other niches unsatisfied. Less optimal but equally myopic policies may actually lead to better collective behavior in the sense that both the brokers and the consumers have higher average utilities overall. However, the underlying myopia still makes the system inherently unstable, and periods of relative calm and prosperity will necessarily be punctuated sporadically with price wars.

Three main ingredients drive these instabilities: the multi-peaked nature of the profit landscape, the ability of well-informed agents to discover and jump nimbly to better peaks in that landscape, and the inability of myopic agents to anticipate the retaliatory response of other agents. These characteristics appear to be generic enough to raise the concern that many types of software agent economies will be plagued with such instabilities.

Consider the first of these three factors. In our model, a broker's ability to unilaterally reject unprofitable customer relationships helped to create the ``expensive'' hump in Figures 2 and 3. The capacity constraint in Edgeworth's model also leads to multiple peaks. Our own study of an entirely different model involving a vertically differentiated product reveals multi-peaked landscapes as well. The existence of so many different mechanisms for creating them leads us to suppose that multi-peaked landscapes may actually be the norm.

In realistic large-scale distributed agent systems, no single agent will have perfect information about the system, and even an omniscient agent might find it infeasible to compute the profit landscape perfectly. However, the present study shows that instabilities can persist even when decisions are made imperfectly. For the economy to be unstable, it is only necessary that agents be able to jump to better (not necessarily optimal) peaks in the landscape. Note that agents will be strongly motivated to obtain the best possible information and to employ the best possible decision algorithms, and this selfish pursuit of individual optimality will threaten the overall stability of the agent economy.

The third factor, myopia, may be curable. One possibility is to endow agents with a predictive algorithm based on some form of machine learning. The agent could base its decisions on its estimation of what will happen over some discounted future horizon. Our preliminary (unpublished) efforts in this area indicate that, under some conditions, price wars can be eliminated in two-broker systems. However, strict application of our particular method to larger systems would be computationally infeasible. The collective dynamics of an economy of co-evolving machine learners are certain to be fascinating, and an important topic for further research.

If we believe that agent economies are susceptible to price-war instabilities, how can we explain the relative infrequency of price wars in human economies? The economics literature provides several possible explanations [Tirole, 1988], including explicit or tacit collusion (based upon foresight), and a variety of frictional effects. The latter include the cost to sellers of updating prices or modifying products, the cost to consumers of shopping for good bargains, and spatial or informational differentiation of products (i.e. different consumers might value the same good differently, depending on their physical location or knowledge).

We believe that these and other mitigating factors that may hold price-war instabilities in check in human economies are likely to be weaker in agent-based economies. Humans are almost certainly more accurate than software agents in predicting the likely effect of their actions upon others. In agent-based information economies, frictional effects like consumer inertia are likely to be much less when agents rather than people are doing the shopping, and updates to prices and products of information goods and services can be made and advertised much more quickly. Localization effects should be much smaller for information goods and services than they are for carrots and carwashes.

Perhaps some unanticipated effect will naturally hinder price and niche wars in information economies. But even if no such factor presents itself, we hope that our continued efforts to understand these undesirable instabilities will lead to methods for controlling them.