On a participation structure that ensures representative prices in prediction markets

The logarithmic market scoring rule (LMSR) is now the de facto market-maker mechanism for prediction markets. We show how LMSR can have more representative final prices by simply imposing a participation structure where the market proceeds in rounds and, in each round, traders can only trade up to a fixed number of contracts. Focusing on markets over binary outcomes, we prove that under such a participation structure, the market price converges after a finite number of rounds to the median of traders' private information for an odd number of traders, and to a point in the median interval for an even number of traders. Thus, the final market price effectively represents all agents' private information since those equilibria are measures of central tendency. We also show that when traders use market price data to revise their private information, the aforementioned equilibrium prices do not change for a broad class of learning methods.