Representing Aggregate Belief through the Competitive Equilibrium of a Securities Market
This provides a mechanism for belief aggregation in multiagent systems, addressing agent incentives and offering a decision-theoretic foundation for expert weights, though it is incremental as it builds on existing market and aggregation methods.
The paper tackles the problem of aggregating probabilistic beliefs from multiple agents by proposing a market-based approach where agents trade securities on uncertain events, and shows that equilibrium prices represent aggregate beliefs with desirable properties for constant risk aversion agents.
We consider the problem of belief aggregation: given a group of individual agents with probabilistic beliefs over a set of uncertain events, formulate a sensible consensus or aggregate probability distribution over these events. Researchers have proposed many aggregation methods, although on the question of which is best the general consensus is that there is no consensus. We develop a market-based approach to this problem, where agents bet on uncertain events by buying or selling securities contingent on their outcomes. Each agent acts in the market so as to maximize expected utility at given securities prices, limited in its activity only by its own risk aversion. The equilibrium prices of goods in this market represent aggregate beliefs. For agents with constant risk aversion, we demonstrate that the aggregate probability exhibits several desirable properties, and is related to independently motivated techniques. We argue that the market-based approach provides a plausible mechanism for belief aggregation in multiagent systems, as it directly addresses self-motivated agent incentives for participation and for truthfulness, and can provide a decision-theoretic foundation for the "expert weights" often employed in centralized pooling techniques.