A Simple Example

Identical Agents Acting in Sequence

Note: in order to run the simulation referred to in this slide, go here, to the Java Applet version. You will be directed to download the latest version of the Java plug-in.

Suppose that every agent has to make a decision between adopting or not adopting a particular behavior. The behavior is either beneficial or detrimental, with equal probability. The agents make their decisions in sequence, one after the other. Every one of them has, essentially, two sources of information: the publicly observable actions of other agents, and his or her own private estimate of whether adopting the behavior is desirable.

Let us add the assumption that each agent is rational, and knows that others are as well. He also knows how precise the estimates of other agents are. The only thing he doesn't know is which way the other agents' private estimates are pointing: towards rejection or towards adoption of the behavior. The agent can compare the reliabilities of the two sources of information available to him, and makes the rational decision of following the source of information that's more reliable.

The society to the left simulates just such a scenario. For an analogy, you may also suppose that a set of individuals is selecting between two restaurants, as you did in the introduction. They do this in a sequence, and everyone sees the actions of his predecessors. Each one knows that all of them are equally good at estimating which restaurant is better. Press the "Go" button several times to see how the society progresses.

The different-looking circle and boolean display to the circle's right represent the reality these agents are operating in; if the displayed boolean is a "T", that tells us that objectively, the new behavior would be beneficial. On the other hand, if it's an "F", the behavior would be detrimental. The yellow portion of each agent represent the amount of information he has about this true concept from his own private sources. Specifically, we record the agent's initial belief of the probability the behavior is beneficial. On the other hand, the blue portion represents the information the agent receives from the actions of other agents. We record the computed probability that the proposition is beneficial based only on the actions of previous agents. This is done through Bayesian updating. When "T" appears in an agent's boolean display, he's made a decision to adopt the behavior. When "F" appears instead, he's decided to reject it.

Keep in mind that this simulation is probabilistic; many different results are possible for each run. In virtually all cases, however, by the time the ninth agent makes a decision, he is part of an informational cascade. At any point, we can tell that an informational cascade is occurring if the blue portion of the information available to the agent is larger than the yellow portion. When that happens, the agent makes a decision based on the public information, regardless of what his private information tells him. As a result, this agent adds no new information to the system and exactly the same amount of public information is available to the next agent. Hence, the status quo is maintained.

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