Projects in Previous Years

1st Semester 2006/07: Preference Representation and Interactive Epistemology

Olivier Roy

If you are interested in this project, please contact Olivier Roy by e-mail.
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).
  Two short survey papers (5-10 pages) about literature relevant to both parts of the course. Further details will be discussed during the first lecture.
  • J. von Neumann  & O. Morgenstern, Theory of Games and Economic Behavior, Princeton UP, 1947
  • L. Savage, The Foundation of Statistics, Dover, 1954
  • R. Jeffrey, The Logic of Decision, Chicago UP, 1983
  • F. J. Anscombe & R. Aumann, A definition of subjective probability, Annals Math. Stat., 1963
  • D. de Jongh & F. Liu, Optimality, Belief and Preference, in Proceedings of ESSLLI  Workshop Rationality and Knowledge, 2006
  • J. van Benthem, P. Girard & O. Roy, Ceteris Paribus Logic, working paper
  • R. Aumann & A. Brandenburger, Epistemic Conditions for Nash Equilibrium, Econometrica, 63, 1995
  • R Aumann, Backward induction and common knowledge of rationality, Games and Economic Behavior, 1995
  • J. van Benthem, S. van Otterloo & O. Roy, Preference logic, conditionals and solution concepts in games, in Festschrift for Krister Segerberg, University of Uppsala, 2005