### NEWS

I hope you enjoyed the course! Please email me with any comments or questions you have about the topics discussed during the course.

Lecturers: Eric Pacuit ( website)
Venue: European Summer School for Logic, Language and Information

Meeting Times: August 6 - 10, 17:00 - 18:30

Location: Opole, Poland

## Overview

Much of the work in traditional game theory is focused on the analysis of solution concepts (typical examples include the Nash equilibrium and its refinements or the various notions of iterated dominance). A solution concept is intended to represent the rational" outcome of a strategic interactive situation. That is, it is what (ideally) rational players would do in the situation being modeled. This course will focus on a key foundational question: How do the (rational or not-so rational) players decide what to do in a strategic situation? This has both a normative component (What are the normative principles that guide the players' decision making?) and a descriptive component (Which psychological phenomena best explain discrepancies between predicted and observed behavior in game situations?).

One approach to this question is found in the literature on the epistemic foundations of solution concepts (for an overview, see this course). The key idea here is to explicitly describe the "informational context" of a game situation (what the players think each other will do, think each other thinks each other will do, and so on) and then derive the fact that the players' choices adhere to a given solution concept from an epistemic property (eg., common belief of rationality). But, a question still remains: How do the players arrive at a particular informational context? In this course, we will study the underlying deliberation process that lead the players to a "rational" choice in a game situation.

The main challenge is to find the balance between descriptive accuracy and normative relevance. While this is true for all theories of individual decision making and reasoning, focusing on game situations raises a number of compelling issues that many students at ESSLLI will find interesting. Robert Aumann and Jacques Dreze adeptly summarize one of the most pressing issues when they write: "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" (R. Aumann and J. Dreze, "Rational Expectations in Games", American Economic Review 2008, 98:1, pgs. 72-86). 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 goal of this course is to introduce and critically examine different models of "rational deliberation" in game situations.

The primary objective of this course is to provide a comprehensive overview of formal models of reasoning in game situations drawing on (recent) literature in game theory, behavioral economics, cognitive science and dynamic epistemic logic. Such an interdisciplinary perspective will appeal to many of the participants at ESSLLI. Students attending this course will see examples of how (dynamic epistemic) logic can be used to model reasoning in strategic situations, understand how methods from the mathematical theory of evolution can provide a powerful tool to explain strategic interactions; and be exposed to intriguing experimental results about how humans behave in strategic situations.

The course will be based on the following papers and books. Additional reading material will be listed in the schedule below.

## Schedule

Below is a schedule for the course (which is subject to change) that will contain links to any handouts, slides and relevant papers for each lecture.

Date Topic
Day 1
August 6, 2012

Slides

Topic: Introduction, Motivation and Background

The following were mentioned in passing and I assume that you have some familiarity with each of these topics: (subjective) probability, von Neumann-Morgenstern utility, expected utility, strategic/extensive form games, Nash equilibrium

The primary focus today was to motivate the study of deliberation and reasoning in games. Along the way, we touched on issues of equilibrium refinement program and discussed a number of conceptual issues concerning reasoning and deliberation in game and decision theory

Day 2
August 7, 2012

Slides

Topic: The Dynamics of Rational Deliberation

We discussed the basic details of Skyrms model of Bayesian deliberators playing a game. Contact me if you would like the python code of my implementation.

Day 3
August 8, 2012

Slides

Topic: Reasoning to a Solution: Common Modes of Reasoning in Games

Day 4
August 9, 2012

Slides

Topic: Reasoning to a Model: Iterated Belief Change as Deliberation

Day 5
August 10, 2012

Slides

Topic: Reasoning in Specific Games: Experimental Results