Market efficiency and learning in an endogenously unstable environment
A least-squares model governs the learning process as traders attempt to extract private information from the market price of an asset. Replicator dynamics govern the evolution of the popularity of this strategy against the alternative, directly acquiring the private information through research. The lack of a fixed point to the dual dynamics embodies the Grossman and Stiglitz (1980) impossibility of informationally efficient markets. The asymptotic behavior of the system has the model switching between price stability and instability, endogenously generating noise in the price. The asymptotic behavior is the same when all traders access and employ both fundamental and market information.
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