# Game Theory

## Conflict exists not just in most economic scenarios but in almost every human interaction, be it economic, political or social and this course will adopt that broad perspective in developing analyses, results and insights.

This course is designed for students with a background in microeconomic theory and will be taught at the intermediate level. The topic of this course, Game Theory, is an essential tool for analyzing strategic interactions between economic agents. It can help us explain anything from why farmers overgraze a common piece of land to the price at which a buyer and seller agree to trade. This course equips students with the skills to use game theory to model real world scenarios and apply game
theoretic methods to solve these models.

This course is aimed at students studying Economics at University but it is also suitable for Mathematics students.

### Syllabus and Course Overview

During this course students will be exposed to non-cooperative game theory, evolutionary game theory and cooperative game theory. Throughout the majority of the course, we assume hyper-rational agents acting in their own interest as we give students a firm grounding in the logic and methods of non-cooperative game theory. We apply standard techniques such as domination of strategies, Nash Equilibrium and backwards induction across a wide variety of games. When relaxing this hyper-rationality assumption, students will then see how evolutionary game theory gives very similar predictions and thus offers a second justification of Nash Equilibrium. Although, we go slightly further to argue that some equilibria are more stable than others.

As will be seen, in many games like the Prisoner’s Dilemma, game theory predicts suboptimal outcomes, since each agent acts in their self-interest, which may not be the common interest. One way to escape this is to allow agents to write binding contracts with each other, which enables us to shift the focus from strategies to payoffs. We take a brief venture into cooperative game theory to see how agents will split the gains from forming coalitions.

One common application of game theory is to bargaining. This pertains to any situation whereby two or more agents have an incentive to reach a mutually beneficial agreement, but conflicting interests over the terms of such an agreement. Students will see some of the myriad of situations bargaining theory can be applied to and learn what predictions bargaining theory can help us make about how these situations will be resolved.

The topics to be covered include:

• What game theory is about and why it is “right”
• How to translate a real world scenario into a game theoretic model
• Expected utility theory
• Simultaneous and sequential move games
• Nash Equilibrium
• Domination of strategies
• Backwards Induction
• Games of Incomplete Information
• Mixed strategies
• Evolutionary game theory
• Cooperative game theory
• Models of bargaining
• Bertrand Model
• Cournot Model
• Repeated Games

### Course Aims

As students will discover, game theory is an essential tool for understanding of a wide range real world phenomena. Among others, this course aims to answer three vital questions:

• What is game theory about?
• How do I apply game theory?
• Why is game theory right?

Students should develop an appreciation for how the details of a game such as when players move and why they know can have a large impact on outcomes.

This course aims to equip students with a wide range of game theoretic skills, which will be used in formulating and solving models of their own. By exposing students to a wide variety of topics and applications, this course gives students some idea of the vast range of phenomena one can use game theory to model and explain. This course will also improve powers of logic and encourage students to think strategically in their future everyday life.

### Learning Outcomes

By the end of this module, students should be able to:

• Understand the different types of games and their uses in strategic thinking.
• Analyse different games and use a variety of tools to find equilibria.
• Understand expected utility theory and the role of probabilities in explaining behaviour.
• Construct models of bargaining and negotiation and how they can be applied to models of competition.
• Distinguish between the different strands of game theory.
• Justify the predictions of non-cooperative game theory an evolutionary perspective.
• Assess the importance of information in games an dhow this can change behaviours.
• Understand the way in which game theoretic models can be applied to a variety of real-world scenarios in economics and in other areas.

### Course Structure

For this course, there will be 4 hours of teaching per day, comprised of lectures and small group teaching. The structure will be:

• 3 hours of lectures.
• A 1 hour seminar in small groups.

Students will also be given time each day for independent study. Towards the end of the third week, students will be provided with time for revision.

### Course Assessment

The module will be assessed via a 2-hour examination. It should be noted that the exam is not compulsory. Everyone who completes the course – whether or not they sit the exam - will receive a certificate of attendance. However, by taking the exam you will also receive a grade/mark for the course which can be helpful to you.

The main course text is:

• K. Binmore; “Playing for Real (coursepack edition)”; 2012; Oxford University Press.

Below are some further readings that students may find helpful for some parts of the course:

• H. Peters; “Game theory: a multi-leveled approach”; 2008; Berlin, Springer.
• J. Weibull, “Evolutionary Game Theory”; 1995; MIT Press.
• A. Muthoo; “Bargaining Theory with Applications”; 1999; Cambridge University Press

### Seminars

Materials will be updated here after each seminar.

Materials will be updated here after each lecture.