Goal. To become familiar with qualitative and quantitative models of preferences used in modal logic and theoretical economics, with representation theorems connecting them, and with epistemic characterizations of game-theoretical solution concepts.
Classical results on foundations of decision theory (von Neumann & Morgenstern 1947, Savage 1954, Jeffrey [1965] 1983, Anscombe and Aumann, 1963) have shown a tight connection between qualitative, i.e. relational, and quantitative, i.e. real-valued utility, representations of preferences. In the first part of this project we are going to study these seminal results, with the aim of understanding their connections with recent work on preferences done in Amsterdam (de Jongh & Liu 2006, van Benthem, Girard & Roy). In the second part of this project we are going to look at the epistemic foundations of game theory (Aumann & Brandenburger 1995, Aumann 1995), in which solution concepts like backward induction and Nash Equilibrium are characterized in terms of the knowledge, beliefs and preferences of the players. Again, we hope to make connections between these results and recent work done in Amsterdam on preference and solution concepts (van Benthem, van Otterloo & Roy, 2005).
