Evolution, Efficiency and Noise Traders in a One-Sided Auction Market

This paper uses an evolutionary approach incorporating the idea of natural selection to examine market behavior in a one-sided buyer auction market. Even with no traders' rationality (such as rational expectations and adaptive learning) and with each trader's behavior preprogrammed with its own inherent and fixed probabilities of overpredicting, predicting correctly and underpredicting the fundamental value of the asset, an informationally efficient market can occur. Traders' behavior is consistent with systematic patterns of judgment biases as documented in the psychological literature. Specifically, shares of one unit of a risky asset are sold at the beginning and liquidated at the end of each time period. The asset's liquidation value is the product of its fundamental value and the exponential of a random shock. Buyers enter the market sequentially over time and each buyer merely acts upon its own inherent and fixed probabilities of overpredicting, predicting correctly and underpredicting the fundamental value. As time goes by there is a constant redistribution of wealth toward buyers who make better predictions. This paper shows that if each buyer's initial wealth is sufficiently small relative to the market supply and if the variation in the random shock to the asset is sufficiently small, then as time gets sufficiently large, the proportion of time, that the asset price is arbitrarily close to the fundamental liquidation value, converges to one with probability one. This conclusion is established under a weak restriction regarding the presence of traders with sufficiently low probabilities of overpredicting the fundamental value.