We apply the average cost optimality equation to zero-sum Markov games, by considering a simple game with one-sided incomplete information that generalizes an example of Aumann and Maschler (1995). We determine the value and identify the optimal strategies for a range of parameters.

We study an in.nitely-repeated .rst-price auction with common values. Initially, bid-ders receive independent private signals about the objects. value, which itself does not change over time. Learning occurs only through observation of the bids. Under one-sided incomplete information, this...