Broker 1 is selected next. Immediately thereafter, all three brokers join in a price war over the 101 configuration, during which the price is ultimately driven down to 0.540. Although the stochasticity of the order in which brokers make decisions causes some variation in the exact details, the price war cycle continues in this fashion indefinitely. A broker participating in the 010 price war receives its expected profit when it undercuts its competitor, and zero when it is being undercut. During the long 101 price war, a broker will be undercut two thirds of the time, and will thus receive just one third of what it expects.
Price wars are clearly harmful to brokers.
In this particular model, they hurt the consumers as well, as illustrated in Fig. During the 010 price war, a single broker is left to offer both categories 1 and 3, which is unsatisfactory to consumers who are highly interested only in one of the two categories. During the long 101 price war, category 2 is completely unavailable to consumers, so the total consumer utility is even lower during this phase than during the 010 price war. Generally, when some or all of the brokers are competing for the same interest vector, a gap is created in the coverage of categories, adversely affecting some consumers. As the number of brokers and consumers in the system grows, the myoptimal strategy becomes completely impractical because of the tremendous demands it makes upon on exact knowledge of the system state, the strategies used by other agents, and computational power.