Game Theory: A Simple Introduction

Game Theory: A Simple Introduction

By K.H. Erickson

Copyright © 2013 K.H. Erickson

All rights reserved.

No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted in any form or by any means, including electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the author.

Also by K.H. Erickson

Simple Introductions

Choice Theory

Financial Economics

Game Theory

Game Theory for Business

Investment Appraisal

Microeconomics

Table of Contents

Introduction

A Game Matrix

The Prisoners’ Dilemma

The Free Rider Problem

Strategic Codependence

Repeated Games and Tit for Tat

Backward Induction

Cartels

Asymmetric Information

Marketing

Fight or Flight

Zero-Sum Games

When Game Theory Fails

Introduction

What exactly is game theory and why is it important? It is a tool used to model interactive decision making, and it shows what’s going on in people’s minds as they interact. It’s used in Mathematics, Economics, Business, Politics, Biology and other disciplines to attempt to make sense of what may at first appear to be irrational behaviour or unexpected outcomes. Game theory suggests that people can always be relied upon to follow their individual incentives and will expect others to do the same, although these incentives will not always lead to the best results. It can offer an explanation as to why people may engage in self-destructive behaviour, consistently achieve worse outcomes than expected, or achieve great results with very little effort.

In simple terms the idea is that life itself is a game and that you and everyone else are playing one hundred percent of the time, whether you want to be or not. It argues that every interaction between two living things sees each make a choice, and that the decision they make depends entirely upon the payoffs or level of gains on offer. Everyone is a player and they’re always trying to stay one step ahead of the competition, using mind games if required. Whether it’s an argument between two lovers, the boss of a company and the job candidate he interviews, a worker deciding how much effort to exert, or a buyer who bids in the last seconds of an auction, they’re all playing the game.

A player can choose between one of two basic options in any interaction: 1) act as an individual; 2) cooperate with the other player. Acting as an individual may involve competing, showing a willingness to compete, or simply not cooperating and instead doing your own thing. It represents some form of rebellion against the other player’s interests. The act of cooperation may involve flight from competition, showing an unwillingness to compete, or actively working with others. It’s not the details that matter but the overall attitude toward rival players.

This book offers a simple and accessible introduction to the basic ideas and applications of game theory. First the basic principles of game theory are presented, from a game matrix and prisoners’ dilemma, to a dominant strategy, Pareto efficiency and the Nash equilibrium. From there asymmetric payoffs and repeated games are explored, along with some of the general tactics and tricks that a player might use to improve their payoffs and their possible outcomes, based largely around the idea of asymmetric information. Mixed strategy and zero-sum games are also examined, with a look at well known games such as hawk-dove, chicken, and interactions between buyers and sellers.

The examples are made clear with over 50 images of the games throughout the book, and characters such as Jack and Jill, friend and stranger, and more are used to keep things interesting and bring the situations to life. The final section looks into some criticisms of the relevance of game theory, and addresses issues of altruism, hatred, and games that change in nature over time.

A Game Matrix

If life itself is a never-ending game then there can be no escape from acting as a player. That makes a focus on long-run outcomes that require investment pointless, as other players can ruin your plans at any moment. The only smart move must be to focus on the short-run process of playing the game, and always keeping your own interests in mind in any interaction.

A game matrix can be used to show the options available in an interaction, the range of potential payoffs on offer for those involved (the players), and the expected outcome. While the matrix is given for an interaction between two players it is applicable for up to any number, and essentially represents what to expect when there are divergent interests. The grid used shows the four possible outcomes that could arise in any interaction, and highlights the expected outcome and the resulting payoffs for players. The four potential outcomes in the game matrix are: both players cooperate; player one cooperates but player two rebels; player two cooperates but player one rebels; and neither player cooperates but instead rebel and seek to go their own way. This is a game matrix without specific players or their payoffs, to show the basic form of the model.

There is a set of two payoff outcomes linked with all four of the possible options, and