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I made two errors in my previous post.
The first is that I put Probability in the utility function. Generally, this is a no no where the E[utility]=sum over i: P(outcome i)*U(outcome i). I therefore changed it to a more simple maximization problem (no Lagrangian multipliers necessary) where the individual maximizes E[Profits].
The second problem has to deal with maximizing subject to probabilities. Since I sampled from the joint posterior distribution of unknown parameters, I had a number of draws from the distribution. What I did in the previous analysis was maximize each pair of simulated draws individually, and then averaged over these maximized results to get what I thought was the optimal result. In general, this method does not result in the optimal value. I should have maximized all pairs simultaneously. Basically I did E[max s of f(s,p)] instead of max s of E[f(s,a)].
In general, the results are superficially similar to my original analysis. Even if the results are largely the same, its best to describe my mistakes upfront, and avoid awkward questions later.
New Code
I made two errors in my previous post.
The first is that I put Probability in the utility function. Generally, this is a no no where the E[utility]=sum over i: P(outcome i)*U(outcome i). I therefore changed it to a more simple maximization problem (no Lagrangian multipliers necessary) where the individual maximizes E[Profits].
The second problem has to deal with maximizing subject to probabilities. Since I sampled from the joint posterior distribution of unknown parameters, I had a number of draws from the distribution. What I did in the previous analysis was maximize each pair of simulated draws individually, and then averaged over these maximized results to get what I thought was the optimal result. In general, this method does not result in the optimal value. I should have maximized all pairs simultaneously. Basically I did E[max s of f(s,p)] instead of max s of E[f(s,a)].
In general, the results are superficially similar to my original analysis. Even if the results are largely the same, its best to describe my mistakes upfront, and avoid awkward questions later.
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