Strategic decision-making under non-probabilistic uncertainty

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The study of decisions made by rational agents in multi-agent systems is a key foundation in the field of game theory. Naturally, the question arises of how agents reason in situations with uncertainty or randomness; this is a frequent topic in the literature but traditionally has been modelled with probability, allowing for exact quantification of uncertainty. However, probability may not necessarily capture all the aspects of uncertainty in a given situation: the common simplifying assumption that all agents have perfect knowledge is unrealistic, and probability can be in a sense too precise to truly capture situations without this assumption. As an example, an uncertainty theory like possibility theory may be a more suitable tool for modelling incomplete information or in systems where uncertainty is somewhat ordinal in nature (i.e. the plausibility of outcomes can only really be qualified against each other). These ideas motivate the proposed PhD: the goal is to explore decision making of agents under uncertainty, especially in such cases that warrant alternatives to probability, and how other methods of modelling uncertainty may impact the outcome of decisions. This will involve investigation of the mathematical basis of systems modelling the reasoning of agents under uncertainty, as well as the computational properties of aspects of these systems. Furthermore, the potential applications of these systems will be looked at.