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 refinement strategies to obtain sensible forecasts about results of uncertain processes. Initially, uncertainty on a system is modeled as the non-deterministic choice of its possible behaviors. Our refinement hypothesis translates non-determinism into imprecise probabilistic choices. Imprecise probabilities allow us to propose a notion of uncertainty refinement in terms of set inclusions. Later on, unpredictability is tackled through a strategic approach using uncertainty profiles and angel/daemon games (𝔞∕𝔡-games). Here, imprecise probabilities form the set of mixed strategies and Nash equilibria corresponds to natural uncertainty refinements. We use this approach to study the performance of Web applications — in terms of response times — under stress conditions.

Keywords

• imprecise and uncertain reasoning
• non-deterministic choice
• refinement
• 𝔞∕𝔡-games
• web orchestrations