Evolution of the prior beliefs in the simple Bayesian hypothesis tests: A selection of the testing agents with the correct beliefs

In general, a successful decision maker need not have been endowed with the correct prior belief on the states of nature. This paper, however, demonstrates that a simple Bayesian hypothesis test scheme has a good property: The probability of a testing agent to obtain the optimal outcome is maximized only if the prior belief of the agent coincides with the "correct" one, when the agent selects the Bayesian-optimal strategy with respect to his or her (own) prior belief. Consequently, in an evolutional setting, where the Bayesian test is conducted repeatedly in parallel by many testing agents with diverse prior beliefs, if the fitness value is determined by the outcome, then only the agents endowed with the correct prior beliefs survive. This result expains why an agent's prior belief can be assumed to coincide with the correct one in the Bayesian hypothesis test, as if the agent knows the true probability that was assigned by nature.