Translation of a Bayesian network to a MarketBayes economy.
The MarketBayes project is an effort to explore the distribution of uncertain
reasoning and decision making in a general setting based on economic market
mechanisms.
The function of markets as aggregators of uncertain belief are well-recognized.
For example, the price of a stock represents the "market evaluation"
of the expected present value of future dividends, and odds in a horse race
aggregate the bettors' beliefs about the winning horse's identity. But despite
their commonality and well-developed underlying theory, there has been little
or no work in the uncertain reasoning community on principled application
of market ideas for distributed uncertain reasoning (but see (Hanson, 1995)
for advocacy of the idea in a related context).
Our basic approach is to set up markets for uncertain propositions, essentially
financial securities that pay off contingent on uncertain events. Agents
bid on these propositions according to their beliefs, subject to their wealth
constraints and tempered by their confidence and risk aversion. In equilibrium,
the market prices can be interpreted as a consensus probability of the participants
in the market.
To investigate this idea, we performed a study of the expressive power of
these kinds of markets compared to standard techniques for probabilistic
reasoning. In particular, we constructed an economic model, called MarketBayes,
that can represent arbitrary joint probability distributions, exploiting
dependence structure in a manner similar to Bayesian networks (Pennock and
Wellman 1996). Given an arbitrary Bayesian network, our algorithm generates
a MarketBayes economy such that the prices of propositions in the unique
competitive equilibrium corresponds exactly to probabilities in the Bayesian
networks.
Our mapping is depicted schematically below. The MarketBayes economy is
comprised of two types of agents, consumers and producers, each of which
bids on a selected set of uncertain propositions (conjunctions of random
variables and their negations). Consumers represent conditional probabilities
in terms of the tradeoff between the conditioning proposition and its conjunction
with the proposition conditioned. The laws of probability are represented
by producers. For example, the producer in the figure arbitrages on the
goods A, AB, and AB', ensuring that the price of the first equals the sum
of prices of the latter two.
MarketBayes has been implemented within our general environment for market-oriented
programming (Wellman 1993). The details of MarketBayes are presented
in our recent article (Pennock and Wellman 1996). Some specific computational
details of early experiments are also described online.