2018 Introduction to Game Theory (Heinrich Nax & Bary Pradelski)

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Project Details

Description:

This course introduces the foundations of game theory. It treats models of social interaction, conflict and cooperation, the origin of cooperation, and concepts of strategic decision making behavior. Examples, applications, and the contrast between theory and empirical results are particularly emphasized.

About Game Theory:

Game theory provides a unified language to study interactions amongst different types of individuals (e.g. humans, firms, nations, animals, etc.). It is often used to analyze situations involving conflict and/or cooperation. The course introduces the basic concepts of both non-cooperative and cooperative game theory (players, strategies, coalitions, rules of games, utilities, etc.) and explains the most prominent game-theoretic solution concepts (Nash equilibrium, sub-game perfection, Core, Shapley Value, etc.). We will also discuss standard extensions (repeated games, incomplete information, evolutionary game theory, signal games, etc.).

In each part of the course, we focus on examples and on selected applications of the theory in different areas. These include analyses of cooperation, social interaction, of institutions and norms, social dilemmas and reciprocity as well as applications on strategic behavior in politics and between countries and companies, the impact of reciprocity, in the labor market, and some applications from biology. Game theory is also applied to control-theoretic problems of transport planning and computer science.

As we present theory and applications, we will also discuss how experimental and other empirical studies have shown that human behavior in the real world often does not meet the strict requirements of rationality from "standard theory", leading us to models of "behavioural" and "experimental" game theory.

Schedule and Course Material
Day Presenter  Lecture   Readings 
 19.02   Heinrich Nax

Introduction: a quick tour of game theory

 Handout

College Admissions and the Stability of Marriage
by D. Gale and L. S. Shapley
 26.02  Heinrich Nax

Cooperative game theory:

  • Core and Shapley value

 Handout

COOPERATIVE GAMES: CORE AND SHAPLEY VALUE
by R. Serrano
 05.03   Bary Pradelski   Prefference and Utilities
  • Utilities
  • Best replies

 Handout

 
 12.03   Bary Pradelski

The Nash equilibrium:

  • Proof
  • Interpretations and refinements

 Handout

 Some of you asked for the connection between utility and entropy, there you go.

Non-cooperative games
by J. F. Nash
 19.03    Bary Pradelski  Non-cooperative game theory: dynamics
  • Sub-game perfection and Bayes-Nash equilibrium
  • Repeated games

 Handout 

 Problems set

 Solutions

 26.03   Bary Pradelski

Game theory: evolution

  • Evolutionary game theory

 Handout

 Automata, matching and foraging behavior of bees 
 09.04  Heinrich Nax

Applications:

  • Interactive Environments and Distributed Control

 Handout

 A Model-Free Approach to Wind Farm Control Using Game Theoretic Methods 
 23.04  Heinrich Nax

Experimental game theory:

  • Behavioral game theory
  • Learning in games
 
 30.04  Heinrich Nax Bargaining
  • Solution concepts
  • Nash program
 
 07.05  Bary Pradelski

Auctions:

  • English, Dutch, Sealed, Open
  • Equivalence and Real-world examples: 3G, Google, etc.
 
 14.05   EXAM  
 28.05        TBA TBA  


Category
Lecture material
Link to experiment demo
Link to user demo