Betting Strategies, Market Selection, and the Wisdom of Crowds

We investigate the limiting behavior of trader wealth and prices in a simple prediction market with a fi-nite set of participants having heterogeneous beliefs. Traders bet repeatedly on the outcome of a binary event with fixed Bernoulli success probability. A class of strategies, including (fractional) Kelly betting and constant relative risk aversion (CRRA) are considered. We show that when traders are willing to risk only a small fraction of their wealth in any period, belief het-erogeneity can persist indefinitely; if bets are large in proportion to wealth then only the most accurate be-lief type survives. The market price is more accurate in the long run when traders with less accurate be-liefs also survive. That is, the survival of traders with heterogeneous beliefs, some less accurate than others, allows the market price to better reflect the objective probability of the event in the long run