# Re: st: RE: [Non Stata] Estimation strategy for a belief learning model.

 From Antoine Terracol To statalist@hsphsun2.harvard.edu Subject Re: st: RE: [Non Stata] Estimation strategy for a belief learning model. Date Mon, 08 Aug 2005 22:22:15 +0200

```Gamma may vary across players since it represents the way the influence of
the opponent's past actions fades as times passes.

f(gamma,X) has a recursive structure:

Belief for strategy A at round t is (assuming data is sorted by player
and by round)

f(gamma,X)=gammaindA/sumg

where

gammaindA=indA[_n-1]+`gamma'*gammaindA[_n-1]

and

sumgu=1+`gamma'*sumgu[_n-1]

(indA = 1 if strategy A has been played by the opponent at round t, and
0 otherwise; and `gamma' is the parameter to be estimated)

A similar updating rule is applied for all other strategies

Antoine.

le 08/08/2005 21:49, austin nichols a ecrit :
> Still unclear.  Does gamma vary across individual players?
> Or is it a parameter of the game structure only?
> Why don't you write out f(g,X) in Stata code for us?
>
> -----Original Message-----
> From: Antoine Terracol [mailto:terracol@univ-paris1.fr]
> Sent: Monday, August 08, 2005 3:31 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: [Non Stata] Estimation strategy for a belief
> learning model.
>
> thanks for your answer, but I think I have been unclear in my first message.
>
> I have a theoretical model for the formation of beliefs, where the
> belief in round t is a function of the past history of the game (denoted
> X), and a gamma parameter, so the "theoretical" belief is f(gamma,X).
> The belief for each strategy is updated independantly of the others
> (i.e. the belief of a given strategy depends only on past occurences of
> the strategy, not on the history of other strategies), but the updating
> rule ensures that beliefs sum up to one.
>
> The players have been asked to report their beliefs, which I label
> "actual" beliefs.
>
> What I want to do is to estimate the gamma parameter using "actual"
> beliefs as the dependant variable, f(gamma,X) and an error term in the RHS:
>
> Actual belief = f(gamma,X) + epsilon
>
> Using this equation, I could estimate the gamma parameter using only
> data on beliefs for a given strategy, but that would be inefficient
> since I would make no use of the information provided by other beliefs.
>
> ...

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