Thinking about rational agents interacting over time is at the center of many research communities represented at ESSLLI. This course will introduce the main research themes and conceptual issues surrounding rational agency. The primary objective is to understand the complex phenomena that arise when rational agents interact and how to incorporate these phenomena into formal models. Studying rational agents involves many different aspects including (but not limited to) action, knowledge, belief, desires, and revision. This course covers all these ingredients toward the goal of understanding how these things work together.
Specific topics that will be introduced (we will focus on topics not represented in other courses at ESSLLI) during the course include 1. logics of knowledge and belief, 2. information dynamics and belief revision, 3. logics of preference and preference change, 4. logics of motivational mental attitudes, and 5. logics of individual and collective action and 6. group phenomena and issues of social choice. In fact, not all parts of this story have been developed within one single discipline. The course will also bring together several research programs: from philosophy, computer science, logic, and game theory, and try to see their various contributions in one coherent manner.
This course is a general introduction to epistemic game theory, with a strong accent on logical approaches to the discipline. We will start by introducing the decision-theoretic background, as well as the game-theoretical basics. We will then move to epistemic game theory proper, by presenting modern logical tools to represent information in interactive contexts, and looking in detail at the classic results in the field, both on so-called strategic form games, "matrices", and extensive form games, "trees". Towards the end of the course, we will connect with the more recent logical literature on information (dynamics), preferences and actions, showing that they offer a new perspective on the game-theoretic results.
The course should be of interest for students in philosophy, computer science (especially multi-agent systems) and linguistics (especially those interested in formal pragmatics). It will be self-contained, thus does not require previous knowledge of the logical or game- and decision-theoretical material that we will cover. We only assume a reasonable level of mathematical maturity.
This course will focus primarily on the following question: how to merge logical systems addressing different aspects of (rational) agency. The first half of the lecture discussed a number of general issues surrounding logics of rational agency. We also looked in some detail about a fair division algorithm called Adjusted Winner (eg., discussed the fact that Adjusted Winner is proportional, envy-free and Pareto efficient. Also we discussed an example demonstrating that agents can manipulate the outcome by misrepresenting their preferences (although being truthful is the only way to guarantee at least 50%).
The second half of the course was a very quick introduction to modal logic. We introduced the basic semantics and discussed what the basic modal language can and cannot express.
Todays lecture introduced a number of (modal) logics for reasoning about different aspects of agency. We spent most of the time discussing the main intuitions underlying the specific formalisms. We discussed epistemic logic, propositional dynamic logic (as a logic of action), and stit logics and logics of agency.