Reasoning in Games

Lecturer: Eric Pacuit (website)
Meeting Times: 9:00 - 10:30
Location: Universitat Pompeu Fabra, Barcelona, Spain
Meeting Room: 52.015

Course Description

This course is a general introduction to game theory with a special focus on the growing body of literature on epistemic game theory. Epistemic game theory aims at formalizing assumptions about knowledge, belief and rationality, and then studies their behavioral implications in games. One standard assumption is that there is common belief of rationality among all the relevant players. A second, related, assumption is adeptly summarized by Robert Aumann and Jacques Dreze in a recent article (Rational Expectations in Games, American Economic Review, 98 (2008), pp. 72-86): "the fundamental insight of game theory [is] that a rational player must take into account that the players reason about each other in deciding how to play". Exactly how the players (should) incorporate the fact that they are interacting with other (actively reasoning) agents into their own decision making process is the subject of much debate. The course will focus on formal models of strategic reasoning in game-theoretic situations.

Some previous exposure to game and decision theory will be helpful, but is not required (I will do my best to provide the necessary background in game and decision theory. This will include a tutorial on the basic concepts of game and decision theory during the first lecture and additional lectures on background material as needed during the course). This is an interdisciplinary topic, and so our readings will be taken from economics, logic, philosophy and cognitive science journals.

An overview of many of the topics discussed in this course can be found here:

Eric Pacuit and Olivier Roy, Epistemic Foundations of Game Theory, The Stanford Encyclopedia of Philosophy (Spring 2015 Edition), Edward N. Zalta (ed.).

Day 1: Decision Theory

Slides

I introduced the basics of decision theory: Decision problems, strict/weak dominance, expected utility, minmax regret, ordinal/cardinal utilities. We discussed the von Neumann-Morgenstern Theorem and Newcomb's paradox. We concluded with a brief discussion of ratifiability (focusing on the Death in Damascus problem).

Background Reading

Day 2: From Decisions to Games

Slides

This lecture introduced the basic concepts of game theory (e.g., strategic and extensive games, Nash equilibrium, iterated strict/weak dominance, rationalizability).

Background Reading
  • K.R. Apt (2011). A Primer on Strategic Games, in Lectures in Game Theory for Computer Scientists, Cambridge University Press, pgs. 1 - 33.
  • Online game theory course by Kevin Leyton-Brown, Matthew Jackson and Yoav Shoham (the website contains a link to a youtube channel containing the video lectures from the course).

Day 3: Game Models

Slides

The lecture introduced epistemic models of games. We discussed epistemic characterizations of Nash equilibrium, correlated equilibrium, iterated strict/weak dominance.

Background Reading
  • EP and O. Roy, Epistemic Foundations of Game Theory, Stanford Encyclopedia of Philosophy, 2015
  • A. Perea, Epistemic Game Theory: Reasoning and Choice, Cambridge University Press, 2012

Day 4: Deliberation (in Games)

Slides

This lecture introduced Brian Skyrms' model of deliberation in games. We discussed a number of extensions of the model. We also briefly discussed how to incorporate belief revision in game models.

Background Reading

Day 5: Backward and Forward Induction, Concluding Remarks

Slides

The main part of the lecture focused on epistemic issues that arise when characterizing forward and backward induction on extensive games. I ended with a few concluding remarks.

Backward Induction