See this interesting paper on Econometrica:
If You're So Smart, Why Aren't You Rich?Belief Selection in Complete and Incomplete Markets,
by Lawrence Blume and David Easley
This paper provides an analysis of the asymptotic properties ofPareto optimal consumption allocations in a stochastic general equilibriummodel with heterogeneous consumers. In particular we investigate the marketselection hypothesis, that markets favor traders with more accurate beliefs.We show that in any Pareto optimal allocation whether each consumer van-ishes or survives is determined entirely by discount factors and beliefs. Sinceequilibrium allocations in economies with complete markets are Pareto opti-mal, our results characterize the limit behavior of these economies. We showthat, all else equal, the market selects for consumers who use Bayesian learn-ing with the truth in the support of their prior and selects among Bayesiansaccording to the size of their parameter space. Finally, we show that ineconomies with incomplete markets these conclusions may not hold. Withincomplete markets payo functions can matter for long run survival, andthe market selection hypothesis fails.
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