Reasoning, games, action, and rationality

Starting from the work of Ramsey (1926); de Finetti (1937); von Neumann and Morgenstern (1944) and Savage (1954), the formal analyses carried in decision and game theory have provided important insights for the theory of rational decision making. More recently, the epistemic program in game theory (Harsanyi, 1967-68; Aumann, 1999; Brandenburger, 2007) has highlighted the importance of mutual expectations for the understanding of interactive rationality, that is for rational decision making in situation of social interaction.

Game theory has inherited from decision theory its instrumental stance on rationality. In both disciplines to choose rationally is to choose, in the light of one’s expectations, the best means to achieve one’s ends. Decision theory studies instrumental rationality in situations where one agent chooses among various actions on the basis of their expected consequences. Crucially, in decision theoretic scenario it is the agent’s environment, or “Nature”, which determines the consequences of his actions. Game theory, on the other hand, is concerned with the interaction of many rational decision makers. Here the consequences of one agent’s decision depends on the choices of all the agents involved in the situation. The expectations of an individual each decision makers are thus no more about a “passive” or “external” environment, but rather about the choices and thus also expectations of other rational decision makers.

Acknowledging this apparently small difference, one vs many agents, complicates the picture of instrumental rationality. In games the players’ expectations become interrelated: what one expects from his opponents depends on what one thinks the others expect from him, and what the others expect from a given player depends on what they think his expectations about them are. Dynamic epistemic logic provides here a fruitful environment to study such entangled expectations. It allows for an elegant analysis of information and information about information, that is of higher-order information.

In this course we will study various foundational issues that arise from the epistemic outlook on games, and show how dynamic epistemic logic (Plaza, 1989; Baltag et al., 1998; van Benthem, 2003; van Ditmarsch et al., 2007) sheds new lights on them. We will, in other words, take a “logical” perspective on conceptual problems regarding the notion of rationality, expectations and choices in interactive situations. The kind of problems that we are interested in and the methods we draw from make the present course a contribution to contemporary formal epistemology (Fitelson, 2006; Hendricks, 2006), while our emphasis on interaction and is also relevant for social software Parikh (2002).

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.