Strategic decision-making under non-probabilistic uncertainty

研究多智能体系统中理性智能体的决策是博弈论领域的一个重要基础。自然地，问题出现了：代理人如何在不确定或随机的情况下进行推理；这是一个经常出现在文献中的话题，但传统上是用概率建模的，允许对不确定性进行精确的量化。然而，概率不一定能捕获给定情况下不确定性的所有方面：所有智能体都拥有完美知识的常见简化假设是不现实的，并且在某种意义上，概率可能过于精确而无法真正捕获没有这种假设的情况。例如，像可能性理论这样的不确定性理论可能是一个更合适的工具，用于建模不完全信息或在不确定性在本质上是有序的系统中（即结果的合理性只能真正相互限定）。这些想法激发了博士学位的提出：目标是探索不确定性下的代理决策，特别是在保证概率选择的情况下，以及其他建模不确定性的方法如何影响决策的结果。这将涉及对不确定性下代理推理系统建模的数学基础的研究，以及这些系统各方面的计算特性。此外，还将研究这些系统的潜在应用。

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.