Dear Prof. Borocco,

                                   I have to say, pardon me if my remark is way off, that there are so many papers which show that REE exists. In fact , the Danthine Donaldson papers show in a macroeconomic output dynamic system with aggregate random shocks that an equilibrium exists. There is a large body of literature in Macroeconomics and Monetary Theory most notably the Lucas helicopter drop model where REE exists with aggregate money shocks. Now If agents have partial information about  w they will be optimising with respect to their observed values of s with expected utility formulations and then there will be a straight forward REE like Radner equilibrium where the market information will aggregate all private information but there is no real mechanism in your problem to reveal all information, public and private, because precisely as you say agents are of diverse risk aversion, which would mean that insuring against risk will also be an objective of the optimisation exercise. You can take a look at some of my papers on my RG page where I have solved close problems for financial especially stock markets under Econophysics methodology, somewhat developed by me, if you don't take exception to it, and you are gladly invited to take a look. There are computations of certain REE type equilibria of course with physical constraints like incomplete markets and bounded rational expected utility methods and computerised information processing using algorithms in time and space with explicit particular information and energy fields. You will see that pooling REE like equilibrium, in many of such environments and fundamentals driven economies, is certainly possible empirically and experimentally. Earl Prof. (University Institute Chair) Dr. (D.Phil.) SKM QC EPS Fellow (Indirect) MRES MES MAICTE

I am not professor, just PhD student but I appreciate it. I have a bayesian linear equilibrium but I am not sure if it is fully revealing.

The following comment that you made is interesting:

but there is no real mechanism in your problem to reveal all information, public and private, because precisely as you say agents are of diverse risk aversion, which would mean that insuring against risk will also be an objective of the optimisation exercise."

Because in Bray (1981) says:

"The first theorem which I prove establishes a set of necessary and sufficient conditions for the futures price to be a sufficient statistic for information about the spot price. .This establishes that the strong symmetry assumptions made about the information structure in the earlier models, and the identical risk aversion assumptions of Danthine [4], and Grossman and Stiglitz [10] are not necessary for their results".

Her first theorem is a consequence of the sufficiency with a normal distribution. The last one implies two things:

I think I will have to check when the conditional expectations and variances are equal for the two following information (futures price, most precise signal). Because according to the Blackwell theorem, the most precise signal is the most sufficient.

If you have any paper on the topic, please share, I would be pleased to read them.

Dear Mr. Borocco,

                               I would like to bring to your kind notice my published paper on Implementing Pareto Optimal Asset Prices which has been published in Quantitative Finance as an Archived Paper and which is listed on my RG page which may give you some clues as to your problem of computing REE using sufficient statistics. You may get some help out of it. Thanks for drawing my attention to your problem, good luck. Earl Prof. (Sir Ashutosh Mukherjee University Institute Chair) Dr. (D.Phil.) SKM QC EPS Fellow (Indirect) MES MRES MAICTE

Thanks, I will look at it.