MarketBayes: A Distributed, Market-Based Bayesian Network

This paper presents initial work on a system called MarketBayes, a computational market economy where distributed agents trade in uncertain propositions. For any Bayesian network, we have defined a corresponding economy of goods, consumers and producers that essentially “computes” the same information. Although our research thus far has only verified the existence of a market structure capable of Bayesian calculations, our hope is that such a system may address a variety of interesting problems of distributed uncertain reasoning. For example, the economic framework should be well suited for belief aggregation, since the bids of numerous agents with varying beliefs, confidence levels and wealth are concisely “summarized” in the going prices of goods. A Bayesian network structure consists of a set of related propositions with information about how the probabilities of the propositions depend on one another. In a MarketBayes economy, the goods to be bought and sold correspond to these propositions. If a proposition is true, the corresponding good is worth one “dollar”; if the proposition is false, it is worth nothing. Then if the proposition is uncertain, its worth should be exactly the probability that it is true (Hanson 1995), assuming risk neutrality. A MarketBayes economy is a set of goods along with a mix of consumers and producers that trade in these goods. After equilibrium is reached, the prices of the propositions should equal the probabilities that the propositions are true. In a Bayesian network, links between propositions encode conditional probabilities. For example a single link from proposition A to proposition B is accompanied by the information P(BIA) = k where k is some probability. The same equation can be rewritten as: