# Estatica

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”Herd Behavior”

Final work to the subject:
“Game Theory”
Teacher: Federico Montes

Presented by:
Manuela Salazar Villegas
Kristyan Aponte

Semester I, 2011
Explanation of herd behavior:
The question that this game tries to solve is: how people take decisions in the society?
As we know, it’s normal that economics agents imitate the actions from others agents, this can be explain by the human tendency to create icons or behavior guidelines since our childhood. For example when we’re going to lunch and we have to pick between two restaurants, one crowded and the other almost empty, we think immediately that it’s better to lunch in
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So we wonder how this person is going to use this information to update his believes. So, in this study we suppose that when he receives new information, he will update his believes by the Bayes rule.蜉
: set of different states of nature.蜉
P(): is the probability known by the agent
The person doesn’t know which of the state of nature that happens was, but he receives a signal that informs him which is the state.
When he receives the signal, the probability of it’s up date, so we use the Bayes rule:蜉

If there is only two states of nature: , the Bayes rules implies:蜉

When there is only two states of nature, it’s useful to considerate the rate of verisimilitude and we have:蜉

So, we have the distribution of the s signal:蜉

So when we apply Bayes rule we have:蜉

We suppose that this signal is symmetrical and his quality is , that means that .
Every agent chooses the action that maximizes his utility:蜉 蜉
The agent doesn’t know what happened, so we suppose that he maximizes his expected utility. The expected value it’s calculate with the private information from every agent. So:蜉 represents the private believe of every t agent蜉
The state of nature is: 蜉
He chooses the action only if: 蜉
That means:

Or,

Where:

We remember that the private probability distribution from the t agent it’s calculating by updating with the BAYES rule. So if represents this probability:蜉 if,

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