General Description

This course will examine a number of the important foundational debates in Game Theory, and the possibility for logic, especially (dynamic) epistemic logic, to contribute to these. We will, more precisely, investigate the following issues:

• The role of mutual expectations in strategic reasoning.
• The place of individual vs. group or team reasoning in coordination.
  
• The role of correlated beliefs, focal points and emotions in reciprocation games or prisoner's dilemmas.
  

The course will be for the most part self-contained. The necessary logics along with the important game-theoretic results and concepts will be introduced. Some previous exposure to modal logic and to the basis of game theory (strategic games, Nash equilibrium and other solutions concepts) is, however, preferable. In case of doubts please contact me by email.

Assessment

Each participant will have to hand in two short papers, maximum 7 pages, by February 4. One of them is expected to be a survey paper, covering a logical or a game-theoretical "solution" to one of the debates presented in class. The other should be more a personal contribution to one of these debates.

Schedule

There will be four lectures, and one session for presentations.

1. Wednesday January 9th. 11.30-13.30.
   Mutual expectations in strategic interaction.
   
   • General introduction to games in strategic forms.
     
   • The "problem" of mutual expectations.
   • Epistemic models for games.


2. Monday January 14th. 11.30-13.30.
   Epistemic characterizations of rational behavior.
   
   • Iterated elimination of strictly dominated strategies, common knowledge of rationality and iterated announcement of rationality.
   • Nash equilibrium, rationality, mutual knowledge of actions and announcement of actions.
     
3. Friday January 18th. 11.30-13.30.
   Reciprocation, correlated beliefs and forward induction.
   
   • Correlated beliefs in strategic games.
   • Forward induction in extensive games.
4. Tuesday January 22nd. 11.30-13.30.
   More on correlated equilibrium.
   
   • The Common Prior assumption: the probabilistic and the relational cases, examples, and discussion/motivations.
     
   • Aumann's theorem(s) : '87 and '05. Examples and discussion.
     
5. Monday January 28th. 11.30-13.30
   
   • Presentations.
     For the presentations, your are expected to give a 10 to 15 min talk on either your survey paper or your personal contribution. If you have doubts or would need more references on the topic please contact me by email.
   • If time permits, I will say a few words about team reasoning.
     

Bibliography

1. Mutual expectations in strategic interaction.
   General introduction to game theory. Both books are available at the UvA library.
   
   • R.B. Myerson. Game Theory: Analysis of Conflict. Harvard University Press, 1997 edition, 1991. See especially chapters 2 and 3.
   • M.J. Osborne and A. Rubinstein. A Course in Game Theory. MIT Press, 1994. See chapter 2 and 6 for the formal definitions.
     
Epistemic logic and epistemic models for games.

• R.J. Aumann. Interactive epistemology I: Knowledge. International Journal of Game Theory, 28:263–300, 1999.
• J. van Benthem. Rational dynamic and epistemic logic in games. In S. Vannucci, editor, Logic, Game Theory and Social Choice III, pages 19–23. University of Siena, department of political economy, 2003. An updated version of this paper is available.
• G. Bonanno. Two lectures on the epistemic foundations of game theory. Delivered at the Royal Netherlands Academy of Arts and Sciences (KNAW), February 8, 2007.
  
• A. Brandenburger. The power of paradox: some recent developments in interactive epistemology. International Journal of Game Theory, 35:465–492, 2007.
• R.J. Aumann. When All is Said and Done, How Should You Play and What Should You Expect? with J. H. Dreze (March 2005, no. 387).
2. Epistemic characterizations of rational behavior.
   Iterated elimination of strictly dominated strategies:
   
   • The references on epistemic models for games.
   • K.R. Apt. The many faces of rationalizability. The B.E. Journal of Theoretical Economics, 7(1), 2007. Article 18.
3. Coordination and team reasoning.
   • R. Sugden. The logic of team reasoning. Philosophical Explanations 6, pages 165–181, 2003.
   • M. Bacharach. Interactive Team Reasoning: a Contribution to the Theory of Cooperation. Research in Economics 23, 117-147, 1999
   • M. Bacharach. Beyond Individual Choices: Teams and Frames in Game Theory. Princeton University Press, Princeton, 2006. Edited by N. Gold and R. Sugden. (not available at the UvA library. Contact me for more information.)
4. Reciprocation, correlated beliefs and forward induction.
   
   • R.J. Aumann. Correlated equilibrium as an expression of bayesian rationality. Econometrica, 55(1-18), 1987.
     
   • Myerson (above), Sections 4.9 and 6.2