Methodology for solving two person game under interval uncertainty

Abstract

In this thesis, robust optimization methodologiesare developed for solving two person zero sum and non zero sum games that consider single or multiple interval inputs (i.e., interval-valued payoffs). Real life problems are not always deterministic and in competitive situations, exact information of competitors is not available. In practice, as the sufficient data from historical sources is quite difficult to obtain, this leads to the games in an uncertain environment. Thus deterministic assumptions about inputs in stochastic environments may lead to infeasibility or poor performance. In such situations, conventional methods that usedeterministic payoffs are not appropriate.Therefore, a method is necessary that can incorporate interval data uncertainty in the analysis of competitive situations. In this thesis,methods for two-person games with interval payoffs have been investigated. The proposed approaches are able to aggregate information from multiple sources and thereby result in more realistic outcomes. The robust optimization methods developed in this thesis can be used to solve two person non-cooperative games with interval-valued (single or multiple intervals) payoffs as well as with single-valued payoffs or a combination of both. A decoupled approach isalso proposed in this thesis to un-nest the robustness-based optimization from the analysis of interval variables to achieve computational efficiency. The proposed methodologies are illustrated with several numerical examples including an investment decision analysis problem.The proposed decoupled approach is compared with some previously developed approaches and it is demonstrated that the proposed formulations generate conservative solutions in the presence of uncertainty.