Comportamiento De Manadas

”Herd Behavior”






Final work to the subject:
“Game Theory”
School: Administration
Mayor: International Business Administration
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 the first one, because the entire people that is inthe crowded restaurant can have some information that we ignore. People that arrive later can have the same reasoning that we had and choose the first restaurant and that’s what we call a Herd.蜉
This problem has been also studied by the psychology, and some psychologists propose different approach. In this explanation, we’re going to considerate that the person has to accommodate in theenvironment and in the same way, he determinates the environment from others agents. In this way, humans can determinate different process of choosing and different process of social learning. It’s interesting to see that animals have similar behaviors when they choose the place to live. So we wonder if it’s possible that rational agents decide to imitate others behavior and then take their own decisionsnot only based on their private information. Birkhchandani, Hirshleifer and Welch (BHW model) had shown that rational agents can generate herd behaviors.蜉
In this write, we’re going to expose three model:
BHW MODEL
LEARNING MODEL WITH A CONTINOUS OF ACTIONS AND SIGNALS
HERD MODEL WITH SOCIAL LEARNING
BHW MODEL
We considerate a situation: the person has to take a decision, but he doesn’t knowsomething important that happens, so he has to take his decision based in his private information and in the history of similar decisions from others or himself. 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 ofnature.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
蜉
If there is only two states of nature: , the Bayes rules implies:蜉


When there is only two states of nature, it’suseful to considerate the rate of verisimilitude and we have:蜉
蜉
So, we have the distribution of the s signal:蜉
蜉
So when we apply Bayes rule we have:蜉
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:
蜉
Or,
蜉
Where:
蜉
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,蜉
And,
if, 蜉
Or, in the same way:
if, 蜉
if, 蜉
That means that the t agent will choose: x=1 only if:蜉
if, 蜉
if, 蜉
Where:
蜉 and, 蜉
In this model there are two definitions and two theorems:
Definition 1:
A herd can exist in a t period if everyone take the same decisions in that period. We have o consider that in a herd agent rationally imitates his predecessors’ behavior.蜉...