Game Theory SS 2013

General Remarks

This is a course on strategic thinking using as its base the models developed in the field of game theory. Applications to public policy and to business strategy will be explored. We will develop the basic tools of game theory through lectures and exercises, and we will put the tools to work by applying them to policy and business examples.

Ojective of the course:

To teach students how to think strategically about a wide range of policy and business problems involving competition, cooperation, bargaining, negotiation etc.
To apply strategic insight to real life problems

Downloads

Lecture 1: Introduction to Game Theory
Lecture 2: Co operative Games - I
Lecture 3: Co operative Games - II
Lecture 4: Non Co operative Games: Solution Concepts - I
Lecture 5: Solution Concepts - II
Lecture 6: Games of Asymmetric Information
Lecture 7: Auction Theory
Lecture 8: Asymmetric Information: Contract Theory
Lecture 9: Strategic Voting
Lecture 10: Network Economics

About Game Theory

Game theory studies competitive and cooperative behavior in strategic environments, where the fortunes of several players are intertwined. It provides methods for identifying optimal strategies and predicting the outcome of strategic interactions. The field of game theory began around 1900 when mathematicians began asking whether there are optimal strategies for parlor games such as chess and poker, and, if so, what these strategies might look like. The first comprehensive formulation of the subject came in 1944 with the publication of the book Theory of Games and Economic Behavior by famous mathematician John von Neumann and eminent economist Oskar Morgenstern. As its title indicates, this book also marked the beginning of the application of game theory to economics. Since then, game theory has been applied to many other fields, including political science, military strategy, law, computer science, and biology, among other areas. In 1994 three pioneers in game theory were awarded a Nobel Prize, marking the 'arrival' of the field. Since then a number of game theorists have been awarded the Nobel highlighting the central role the field has come to occupy in economics. Among the other applications, game theory today is finding its way into the world of business. (Pick up a business magazine or book and there is a good chance that it will use some game theory jargon: zero-sum game, Prisoner's Dilemma, win-win game, etc.) We will be learning the underlying theory in the course, and using it to understand the principles of strategic behaviour in business.

Course Content

The course is divided into two parts: game theoretic tools for analysis and application of the tools to a variety of interactive contexts drawn from business and policy making. The topics covered by the course are given below.

Co Operative Games

Assessing the value of players and coaltions (‘Cooperative Games’)

In this module we assume that players in a game can make binding contracts and ask the basic question: given the ‘value’ of individuals and coalitions what is a rational way to divide the pie between the individual players and what is the likely structure of coalitions that form. We will also discuss alternate ways to allocate costs between various parties.To answer, we will introduce techniques for thinking about such situations and calculating the value of players under different assumptions. Topics covered in this module include definition of the coalitional form of a game, solution concepts like the core, Shapley value etc.

Non Co operative Games

Games with Complete Information

Thinking About What They’re Thinking In this module we begin with an overview of the basic principles of ‘non-cooperative games’. With these games in mind, we then ask the basic question: How can a player choose a good strategy when the best choice depends on what strategies the other players in the game choose? To answer, we will introduce techniques for thinking through the game from the positions of the other players, and anticipating their choices. Topics covered in this module include definition of games in normal and extensive form, principle of dominant strategies and safe strategies, Nash Equilibrium, backward induction equilibrium. Well known games such as the The Prisoner’s Dilemma, the Battle of the Sexes, the Coordination Game …will be studied.

Games with Incomplete Information

Asymmetric Information: Mechanism Designs and Contracts

Mechanism Design In this session, we look at the art of designing rules of a game to achieve a specific outcome. This is done by setting up a structure in which each player has an incentive to behave as the designer intends. After introducing the revelation principle we will apply the theory to the design of financing “public goods” using the Clark Groves mechanism.

Auctions We will study the application of the principles taught in Mechanism Design to optimal design and bidding in auctions. We will start with an overview of the main theoretical results in auction theory like the winners curse and go on to a detailed analysis of Treasury auctions, and telecom license auctions. Finally an analysis of the Vickrey second price auction will set the stage for subsequent module on mechanism design.

The Problem of Adverse selection vs Moral Hazard Often interaction between two parties involves one party at a distinct advantage over the other in terms of access to information. Information asymmetry can arise because types are unknown (adverse selection) or the actions are unobservable (moral hazard). An averaging across different types is inefficient. In this session we will discuss the problem and possible soultions to overcome it.

Strategic Voting In this module we introduce the issues presented by collective decision making through voting like the Condorcet Paradox, the reversal paradox, and the agenda paradox. We study the outcome of elections when we admit the possibility of voters misrepresenting their preferences to ‘rig’ the elections in their favor.

Network Economics Herd behavior---is it entirely irrational or does it pay to be a part of a larger faction. The economics of compatibility and adaptability.

Matching Problem How does one ensure strategic players are matched so that they do not move elsewhere? How to ensure college aspirants and colleges are matched or marriages are stable!