Strategic decision-making under non-probabilistic uncertainty

多智能体系统中理性智能体决策的研究是博弈论领域的重要基础。自然，问题就会出现，即代理人如何在具有不确定性或随机性的情况下进行推理；这是文献中经常讨论的话题，但传统上一直是用概率建模的，从而允许准确地量化不确定性。然而，概率不一定捕捉到给定情况下不确定性的所有方面：常见的简化假设认为所有代理都拥有完美的知识是不现实的，而且在某种意义上，如果没有这一假设，概率可能太精确，无法真正捕捉到情况。例如，像可能性理论这样的不确定性理论可能是更适合于对不完全信息进行建模的工具，或者是在不确定性本质上多少是有序的系统中(即结果的似是而非只能真正相互限定)。这些想法激励了拟议的博士学位：目标是探索不确定条件下代理人的决策，特别是在需要替代概率的情况下，以及其他建模不确定性的方法可能如何影响决策结果。这将涉及研究对不确定情况下代理人的推理进行建模的系统的数学基础，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.