Refining Indeterministic Choice: Imprecise Probabilities and Strategic Thinking

Abstract

Often, uncertainty is present in processes that are part of our routines. Having tools to understand the consequences of unpredictability is convenient. We introduce a general framework to deal with uncertainty in the realm of distribution sets that are descriptions of imprecise probabilities. We propose several non-biased re ̄nement strategies to obtain sensible forecasts about results of uncertain processes. Initially, uncertainty on a system is modeled as the nondeterministic choice of its possible behaviors. Our re ̄nement hypothesis translates non-determinism into imprecise probabilistic choices. Imprecise probabilities allow us to propose a notion of uncertainty re ̄nement in terms of set inclusions. Later on, unpredictability is tackled through a strategic approach using uncertainty pro ̄les and angel/daemon games (a=d-games). Here, imprecise probabilities form the set of mixed strategies and Nash equilibria corresponds to natural uncertainty re ̄nements. We use this approach to study the performance of Web applications in terms of response times under stress conditions.