Dynamic choice in a complex world

We consider an environment in which a Decision Maker (DM) finds it sufficiently complex to even describe the state space, let alone guess the parameters of the underlying data generating process. He is therefore unable to use the standard Bayesian methods. Instead, at each moment in time, the DM constructs a preference relation on the set of available actions based on their past performance. We postulate a set of axioms on this family of...