Christian Espindola: Optimal strategies for coordinated inference

This talk will be a panoramic presentation of the results in Hardin and Taylor recent book "The mathematics of coordinated inference", which studies problems of individuals with partial information which can develop a collective strategy to find out missing pieces of data. One classical example is the usual "hat problem", in which individuals are given hats of different colours and are expected to guess their own hat colour looking only at the colours of the others; in this case it is well known that collective strategies exist that maximize the number of correct guesses. We will review many different generalizations of hat problems involving infinitely many individuals and show how the existence of optimal strategies is closely linked to the axioms of the underlying set theory used to describe them. In particular, we will see that some appeal to the Axiom of Choice is unavoidable in most cases, and describe one hat problem for which the existence of an optimal strategy is equivalent to the Generalized Continuum Hypothesis.