Comparing belief models

One study used Bayesian procedure to draw inferences about the relative accuracy of Cournot and fictitious play. The procedure started with prior probabilities that each of the two theories are true. Then simulations were used to generate likelihoods for different observations. Using the priors, the simulated likelihoods and the actual data, Bayes' rule can be used to infer the posterior probability that each theory is true. This procedure is applied to experiments on dominance-solvable games by Knott and Miller (1987) and coordination games by Cooper et al (1990). Cournot is much worse on a dominance-solvable game and about equally good on a coordination game, so it is much worse overall.

A huge advantage of the Bayesian approach is the ability to naturally integrate results from different experiements. For example, if one theory is much better on one data set and much worse on another, by multiplying the likelihood ratios together (a procedure that assumes experiments are independent, which is sometimes unlikely) it is often possible to declare a clear overall winner rather than simply concluding that one study favoured each theory.

Colin F. Camerer, (2003) Behavioral G ame Theory, Sage, p. 299