Game Theory

Lecturer: Andranik Khachatryan
Classes: 2 Lectures per week

Short Description

Game theory explores strategic situations when one or several players interact.In strategic situations the end result depends on the strategies of all players. For this reason each participant that aims to reach a favorable outcome has to take into account decisions made by other players.
Game theory is widely used in economics, political science and evolutionary biology and in many daily situations.
This is an introductory course. Leaving aside complex mathematical proofs we will focus on examples and applications. We will do many experiments and will play many games in the classroom.

Requirements

Background:: Knowledge of mathematics at the level of 2nd year engineering. Basic knowledge of probability theory. Basic economics knowledge is desirable.
Homework:: Every 1-2 class. The answers must be sent within one or two weeks. Deadlines will be announced during classes.

Textbooks

  1. Prajit K. Dutta: “Strategies and Games: Theory and Practice”
  2. Joel Watson: “Strategy: An Introduction to Game Theory”
  3. Martin J. Osborne: “An Introduction to Game Theory”
  4. Drew Fudenberg and Jean Tirole:“Game Theory”

    Content
    1. Introduction: Games and Strategies: The Normal (matrix) form of games. The “Prisoner’s dilemma’’ game and The “Keynesian beauty contest” game. Dominant strategies. Rational strategies. Rules of the game, common knowledge and beliefs.
    2. Definitions: Types of dominance. Strict, weak and very weak dominance. Iterated elimination of strict dominated strategies.Voter’s Game
    3. Best Response. Beliefs. 11 meter game. Strategic Profile. Mixed Strategies.
    4. Partnership Game.The concept of Nash Equilibrium
    5. Definition of Nash Equilibrium and examples. Investment Game. Coordination, effectiveness, Pareto dominance
    6. Cournot Duopoly. Oligopolies. Plays in a Nash Equilibrium
    7. Evolution. Animal interaction as strategic situations. Evolutionary stable strategies. Hawk-Dove Game. Examples of evolutionary games. Asymmetric roles.
    8. Evolutionary stability and effectiveness. The evolution of social norms. Evolutionary dynamics at the example of Hawk-Dove Game.
    9. Sequential-Move Games.Threats, promises and response rules.
    10. Stackelberg duopoly.Comparison with Cournot. The “Nim” game. The US against ALCOA. NBC against News International.
    11. Duels. Bargaining. Ultimatum bargaining
    12. Repeated games. Strategies for a repeated game. End game effects. Repeated game equilibrium
    13. Coalition games. Shapley value. Coalition game core.
    14. Bayesian games, Imperfect Information Games. Stochastic games. Learning rules.