Heterogenous Agents in a Model
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Effects of Imprecise Beliefs about the Precision of an Agent
Now we explore the effects of another kind of modification to the initial model. Let us say that everyone believes that Agent 9 in the sequence is more intelligent than everyone else, even though the agent himself knows that he is no smarter. We modeled such a society to the left of this text. Agent 9's actual precision is 0.6, just like the precision of every other Agent. However, everyone else believes that Agent 9's precision is 0.9. The two numbers are displayed directly below his circle.
Click the "Go" button several times to see how the society progresses. By the time you reach Agent 9, the society should have entered a cascade. Note that Agent 9 never breaks this cascade. Instead, he always deepens it, which can be seen in the fact that Agent 10's blue circle portion (public knowledge) is larger than that of Agent 8.
There is an easy intuitive explanation of this result. Agent 9 himself knows that he is no more intelligent than the others, and thus makes his decision along with the preceding agents in the cascade. However, Agent 10 believes that Agent 9 is smarter than everyone else, and thus becomes even more convinced of the public opinion than Agent 8 was.
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