## Teacher package: Game theory

The Plus teacher packages are designed to give teachers (and students) easy access to Plus content on a particular subject area. Most Plus articles go far beyond the explicit maths taught at school, while still being accessible to someone doing GCSE and A level maths. They put classroom maths in context by explaining the bigger picture — they explore applications in the real world, find maths in unusual places, and delve into mathematical history and philosophy. We therefore hope that our teacher packages provide an ideal resource for students working on projects and teachers wanting to offer their students a deeper insight into the world of maths.

### Game theory

The Chess Game, by Ludwig Deutsch

Game theory is a great way of sneaking up on maths. You can start off playing an actual game, then start thinking about strategies, and before you know it you're doing proper maths, either conceptually or using equations and formulae. In this teacher package you'll find all our articles on game theory, divided into two categories:

• Game theory under the microscope: These articles take an in-depth look at game theory, including equations and calculations.
• Game theory in the news: These articles report on news about game theory and its applications, giving you an overview of what can be done with it and how.
• ### Game theory under the microscope

Does it pay to be nice? - the maths of altruism — Does it pay to be nice? Yes, it does. And we're not just talking about that warm fuzzy feeling inside, it pays in evolutionary terms of genetic success too. This two part article shows how game theory shows that being nice is unavoidable. Read part I and part II.

Does it pay to be clever? — Why are we so clever? In evolutionary terms this isn't obvious: evolution tends to favour cheap solutions and the human brain is expensive. It consumes about 20% of our body's energy budget yet it only makes up 2% of our body mass. So why did it make evolutionary sense for us humans to develop powerful brains? Game theory provides a possible answer.

The revelation game — Is it rational to believe in a god? The most famous rational argument in favour of belief was made by Blaise Pascal, but what happens if we apply modern game theory to the question?

Maths in a minute: The prisoner's dilemma — A brief introduction to one of game theory's staples.

Games people play — Combinatorial Game Theory is a powerful tool for analysing mathematical games. This article explains how the technique can be used to analyse games such as Twentyone and Nim, and even some chess endgames. A follow-up article, Practice makes perfect, looks at how computers are programmed to play chess.

Blast it like Beckham? — What tactics should a soccer player use when taking a penalty kick? And what can the goalkeeper do to foil his plans? Game theory can give you the answers.

Game theory and the Cuban missile crisis — This article uses the Cuban missile crisis to illustrate the theory of moves, which is not just an abstract mathematical model but one that mirrors the real-life choices, and underlying thinking, of flesh-and-blood decision makers.

If we all go for the blonde — This article revisits a scene from the film A beautiful mind, using game theory to decide on chat-up strategies.

Adam Smith and the invisible hand — Adam Smith is often thought of as the father of modern economics. In his book An inquiry into the nature and causes of the wealth of nations Smith described the "invisible hand" mechanism by which he felt economic society operated. Modern game theory has much to add to Smith's description.

Mathematical mysteries: Survival of the nicest — One of the most puzzling aspects of human behaviour is cooperation in situations where backstabbing and selfishness would seem to be more rewarding. From the point of view of evolutionary theory, the very existence of altruism and cooperation appear mysterious.

The Carol syndrome — Does being attractive guarantee a long line of suitors? This article uses game theory to find out.

### Game theory in the news

Guilt counts — Is the fear of guilt what makes us be nice to other people? Game theorists investigate.

Trust me, I've evolved — Game theorists model the evolution of trust and trustworthiness.

Love's a gamble — Cheap or expensive? On the giving of gifts during courtship.

Leaving the markets — The 2009 Nobel Prize in Economics went to two unusual economists, one of whom used game theory to explore human cooperation.

2007 Nobel Prizes won by mathematicians — In particular, the economics prize went to game theorists who investigated financial markets.

Game theory wins Nobel Prize — The 2005 Nobel Prize went to game theorists who investigated conflict and cooperation.