We now revisit the situation in which all five sellers utilize the
myoptimal pricing strategy, but we allow one of the sellers to reset
its price five times as quickly as all the others. These price
dynamics are illustrated in Fig. 5(a). As in
Fig. 2(a), we experience price wars; in this case, however,
they are accelerated, which is apparent from the increase in the
number of cycles that occur during the simulation run. From the
individual profit curves, which in Fig. 5(b) depict
cumulative profits rather than instantaneous profits, we notice that
the fast myoptimal agent obtains substantially more profit than the
others because it undercuts far more often than it itself is undercut.
Analysis yields that the expected profit for a given myoptimal seller
s who resets its prices at rate 
, assuming all other sellers
are myoptimal, is as follows:
Eq. 11 predicts average profits of 119/960 = 0.1240 for the fast seller and 34/960 = 0.0354 for the slower ones, values which compare reasonably well with those obtained by averaging over the last 10 complete cycles of the price war, namely 0.1111 and 0.0351, respectively.
Figure 5: (a) and (b) Price and profit dynamics, respectively, with 1 Fast MY
pricebot.
Evidently, myoptimal pricebots stand to gain by resetting their prices at faster, rather than slower, rates, particularly when a large proportion of the buyer population is shopbot-assisted (see Eq. 11). If MY pricebots were to reprice their goods with ever-increasing frequency, a sort of arms race would develop, leading to arbitrarily fast price-war cycles. This observation is not specific to myoptimal agents. In additional simulations, we have observed sufficiently fast DF pricebots who obtain the upper hand over slower derivative following and myoptimal agents. In the absence of any throttling mechanism, it is advantageous for pricebots to re-price their goods as quickly as possible.
Let us carry the arms race scenario a bit further. In a world in which sellers are inclined to reset prices at ever-increasing rates, human price setters would undoubtedly be too inefficient. Sellers, therefore, would necessarily come to rely on pricebots, perhaps sophisticated variants of one of the strategies proposed in Sec. 4. Quite possibly, pricebot strategies would utilize information about the buyer population, which could be purchased from other agents. Even more likely, pricebot strategies would require knowledge of their competitors' prices. How would up-to-date information be obtained? From shopbots, of course!
With each seller seeking to re-price its products faster than its competitors, shopbots would quickly become overloaded with requests. Imagine a scenario in which a large player like amazon.com were to use the following simple price-setting strategy: every 10 minutes, submit 2 million or so queries to one or more shopbots (one for each title carried by Amazon.com), then charge 1 cent less than the minimum price returned on each title! Since the job of shopbots is to query individual sellers for prices, it would in turn pass this load back to Amazon.com's competitors. The rate of pricing requests made by sellers could easily dwarf the rate at which similar requests would be made by human buyers, thereby eliminating the potential of shopbots to ameliorate market frictions.
A typical solution to an excess demand for shopbot services would be for shopbots to charge pricebots for price information. Today, shopbots tend to make a living by selling advertising space on their Web pages. This appears to be an adequate business model so long as requests are made by humans. Agents, however, are unwelcome customers because they are are not influenced by advertisements; as a result, agents are either barely tolerated or excluded intentionally. By charging for the information services they provide, shopbots would be economically-motivated agents, creating the proper incentives to deter excess demand, and welcoming business from other agents.
Once shopbots begin to charge for pricing information, it would seem natural for sellers -- the actual owners of the desired information -- to themselves charge shopbots for price information. In fact, sellers could use another form of pricebot to dynamically price this information. This scenario illustrates how the need for agents to dynamically price their services could quickly percolate through an entire economy of software agents. The alternative is ``meltdown'' due to overload which could occur as agents become more prevalent on the Internet. Rules of etiquette followed voluntarily today by web crawlers and related programs [9] could be trampled in the rush for competitive advantage.
