Convergence within binary market scoring rules
Prediction markets are run to extract information from its participants through financial incentive. The market scoring rule mechanism represents a way of organizing markets in order to foster agents to make sincere predictions. Market scoring rules are usually presented in a context of asset trading, but they also boil down to a sequential probability report process analyzed here. If the future state space is binary (i.e. composed of only two possible states) and only two agents participate alternatively in the market, it is proven that for strictly proper market scoring rules, the report sequences of each agent converge toward limit probability reports which are closer to each other than the subjective probabilities of the agents.