Players who have a common interest are engaged in a game with incomplete information. Before playing they get differential signals that stochastically depend on the actual state of nature. These signal not only provide the players with partial information about the state of nature but also serve...

A self-proclaimed expert uses past observations of a stochastic process to make probabilistic predictions about the process. An inspector applies a test function to the infinite sequence of predictions provided by the expert and the observed realization of the process in order to check the...