Puzzles and Paradoxes from Decision and Game Theory

Both decision and game theory have many uses outside of economics. This is especially true at ESSLLI. Both logicians and linguists have used the ideas and mathematical models originally developed by economists to study rational decision making. In this course, I will introduce the puzzles and paradoxes that have a prominent place in the decision and game theory literature. There are two main motivations for offering such a course at ESSLLI.

The first motivation is that this course will serve as a introduction to decision and game theory. However, I will not follow the standard textbook presentation of this material. (For example, as found in -Games and Decisions: Introduction and Critical Survey- by H. Duncan Luce and Howard Raiffa, -Essentials of Game Theory- by Yoav Shoham and Kevin Leyton-Brown or -An Introduction to Decision Theory- by Martin Peterson.) Rather than focusing on the technical details of different formalisms and the main mathematical results, I will focus on the key foundational questions (of course, introducing formal details as needed. Taking an ``issue-oriented" approach to introducing decision and game theory is especially useful for students at a summer school such as ESSLLI. Many of the technical advances in game and decision theory are driven by the analysis of puzzles about decision making and strategic interaction. Different formal frameworks are then judged, in part, on how well they conform to the analyst's intuitions about the relevant set of examples. Thus, in order to appreciate the usefulness and limits of the different mathematical models and results, it is important to understand the issues that motivate the key technical developments.

The second motivation is that a course on foundational issues in decision and game theory touches on many of the themes discussed in other ESSLLI courses. Many people attending ESSLLI will have been exposed to topics such as the semantics of counterfactuals, causal reasoning, reasoning about knowledge and common knowledge of a group of agents, and belief revision (either at ESSLLI or in their previous coursework). The analysis of the puzzles and paradoxes that I will discuss in this course can be viewed as interesting application of these familiar ideas. The puzzles and paradoxes that I will discuss are:

• Paradoxes of expected utility: St. Petersberg paradox, Pasadena game, The Two-envelop paradox
• Allais and Ellsberg paradox
• Newcomb's paradox and the psychopath button problem
• Puzzling games: the Prisoner's Dilemma and the Traveler's Dilemma
• The absent-minded driver problem
• Backward induction and Selten's chain store paradox
• Rubinstein's email game and the general's problem
• Backward induction and common knowledge of rationality
• The Brandenburger-Keisler paradox
• Framing in decision and game theory: language-dependent decisions and games, coordination problems and the theory of focal points.

The course will be of interest for students in logic, 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 game- and decision-theoretical material that we will cover.