Game theory

Game theory and North Korea

Kim Jong-Un is a new leader in a dangerous situation. Hopefully he’s read up on some game theory! There are lots of ways to look at the North Korean situation through the lens of game theory and this post looks … Continue reading

St Petersburg paradox explanation

This is an interesting example from decision theory (which is pretty closely linked to game theory). A (very generous!) casino offers you a game where the pot starts at $1 and on each turn a (fair) coin is tossed. If … Continue reading

Keyboards, kids and game theory

The last few months have been a really exciting time for me because my daughter has just started at school. It is amazing to see how quickly kids learn new things once they are at school. She is learning her … Continue reading

Nim game solution

I have previously worked out a solution to Nim which is a simple game of strategy. The game is played by two players who each take turns to pick up matches from two separate piles. The rules allow a player … Continue reading

Shapley Shubik power index part 2

I have looked previously at the Shapley Shubik power index which defines the power that each voter has depending on the number of votes that they control. This can lead to some very interesting and unexpected results. Imagine that there … Continue reading

Divide and conquer

The Shapley Shubik Power Index With Lloyd Shapley having just won the Nobel prize  it seems like a good time to look at the Shapley-Shubik power index. This is a way to measure how much power different voters have in a … Continue reading

Roth and Shapley Nobel Prize winners

The big news in game theory this week is the Nobel Prize that has been awarded to Al Roth and Lloyd Shapley for their work on market design and matching theory.           Rather than me try … Continue reading

Analysis of UK 2010 elections – Duverger’s Law

I recently wrote about Duverger’s law which explains why a voting system like the one in the US can lead to just two parties surviving. The ‘law’ recognises that people will vote tactically and may not vote for their favourite … Continue reading

Ryder Cup – why the playing order matters

With the Ryder Cup just about to start it is a good time to think about the game theory involved in the selecting the order that the players play in. A lot of time and discussion goes into trying to … Continue reading

Eric Maskin – Harvard professor, his work to date

As Eric Maskin has just been appointed one of only 22 University Professors at Harvard University, this seemed like a good time to have a look back at some of his contributions to game theory. Professor Maskin is one of … Continue reading

Why there are only two major political parties in the US

With the US elections coming up soon, have you ever wondered why there are only two major parties? Is it just a coincidence or is there something more fundamental going on? It fact it is nearly inevitable that the kind … Continue reading

Fair division in the Talmud

My last post looked at the three wives problem from the Talmud. Today I will look at another problem of how to divide up goods also from the Talmud. This one has a very different answer, but there might be … Continue reading

How game theory solved a 2,000 year old problem

The Talmud is one of the central texts of Judaism. It was written around 200 A.D. and yet contains a problem that no-one could understand until two game theory professors solved it. The problem is known as the Three Wives … Continue reading

First mover advantage? Not always…

The order in which players make their decisions in a game can make a huge difference to the outcome. Take the simple game of Nim. In this game there are two players who take it in turns to play. There … Continue reading

John von Neumann’s minimax theory

“Keeping up with him was all but impossible. The feeling was you were on a tricycle chasing a racing car” Israel Halperin on John von Neumann John von Neumann made huge contributions to many areas of mathematics and was also … Continue reading

More roads can mean slower traffic

Does building a big fast road between two towns make the traffic go faster. You would think so but it is not always the case. Imagine that you live in a place called Greenville and you want to get to … Continue reading

Jack Bauer knows game theory

You are undercover and about to make a breakthrough with a mob boss. But your partner, not knowing your mission, tries to save you and gets captured. The boss suspects you might be working with the authorities. He asks you to … Continue reading

Deal or no deal?

The game show Deal or No Deal starts with 15 boxes, each containing an amount of money. The player has one box and gradually eliminates the other 14 boxes. As they reduce the number of boxes in the game they … Continue reading

Parrondo’s Paradox – how losing strategies can win

It is hard to believe but if you combine two losing games then, in some situations, you can turn them into a winning game. This is known as Parrondo’s paradox, named after Juan Parrondo (pictured), a Spanish physicist, who discovered … Continue reading

Strategy lesson from a great Chinese warrior

“Books are only useful in helping me remember my name. Mastering swordsmanship allows me to face only one opponent, so it’s not worth learning. I want to learn how to defeat 10,000 enemies.” Xiang Yu   Xiang Yu was born … Continue reading

Game theory and eBay bidding strategy

What is the best strategy to use when bidding on eBay? I will assume that there are three strategies to choose from: 1 – Bid the maximum price you are willing to pay at the start of the auction and … Continue reading

What is evolutionary game theory?

Two men were the founding fathers of evolutionary game theory. Both their fathers died when they were young, neither studied biology as their first degree and both fought cancer in middle age. George R Price (pictured) trained as a chemist … Continue reading

The most extraordinary true Christmas story ever

With Christmas fast approaching it is nice to look back on an amazing piece of co-operation that took place nearly 100 years ago. Imagine that it is Christmas Eve 1914 and you are a British solider sitting, cold and wet, … Continue reading

Stanford game theory course

If you haven’t seen it yet then check out the online game theory course from Stanford University, starting on March 19th. It’s great to see that thousands of people have already signed up, make it your New Year’s resolution to … Continue reading

Mathematics of a price war

In my last post I looked at two companies competing over a natural monopoly. We saw that once they started competing it would not then make sense for either company to drop out. This is why price wars tend to … Continue reading

Why you won’t win a price war

Today I will look at a simplified situation where two companies are battling over a natural monopoly. Whilst they are both competing the market isn’t big enough for either of them to make a profit. Once one of them drops … Continue reading

Five ways to escape a prisoners dilemma

If you find yourself in a prisoners dilemma there are some ways you can try to get out of it. 1 – Communication In the normal definition of the problem the two prisoners are not able to communicate with each … Continue reading

Game theory and segregation

Would you rather live is a neighborhood where everyone shares your skin color? Most people would say that they are not racist and would prefer to live in a mixed neighborhood. If this is the case then why are most … Continue reading

A – Z of Game Theory

A – Auctions – There are four main types of auction First price sealed bid auctions – everyone puts a bid in a sealed envelope, the highest bid wins and pays the price they bid Second price sealed bid auctions … Continue reading

Introduction to game theory: Perfect information

Perfect information in game theory is when a player who is about to make his move in a game can see all the moves that have been made before. Chess is an example of a game with perfect information as … Continue reading

Top game theory links: September 2, 2011

The Economist: Game theory in practice. Some great examples of people using game theory to make real world decisions: More business applications of game theory from Gravitas: Academic paper on how to deal with free-riders in climate change … Continue reading

Introduction to game theory: Zero sum games

A zero sum game is one where whatever one person gains another person loses. It is called a zero-sum game because each gain by one player, say +$100, is offset by the loss of another, -$100. The two always add … Continue reading

Tactics in bike races

The tactics of big cycle races, such as the Tour de France, provide a fascinating area for game theory to analyze. Each rider has a couple of basic options: He can either wait in the pack and conserve his energy … Continue reading

Top game theory links: August 26th

This week’s top links: Game theory and cyber attacks Game Theory and the Eurozone Crisis: Motivating a gym class using game theory Game theory in mediation:

What kind of dictator are you?

Colonel Gaddafi is a classic example of a selfish dictator taking as much as he can from his powerful position. How would you act if you were a dictator? The dictator game The dictator game is closely related to the … Continue reading

This week’s top game theory links: August 19

Top five links in the last week: Game theory explains the shortage of eligible men Using game theory to understand the stasis in India-Pakistan relations Why Warren Buffett should NEVER pay voluntary additional taxes  The kickstarter effect: Using game theory to … Continue reading

Fair division

How do you make progress when you need to divide something up between two people but they can’t agree on what is a fair split. The classic example is how to fairly cut a cake. The answer is for one … Continue reading

Will the London riots start again?

Will the London riots start again? Game theory says that it’s very unlikely. Riots only start spontaneously when there is a trigger to bring people together on the streets. There is almost no chance of that happening again in London … Continue reading

Why riots start

The recent riots in London and the rest of the UK have seen people in respectable jobs prosecuted. This is surprising to most people but we can use game theory to see how people who would not normally riot might … Continue reading


I’m taking my summer break from blogging for the next week. My next post will be on Monday, August 15. Don’t miss out on future posts: Subscribe by RSS (what is RSS?) or Subscribe by Email Check out some of … Continue reading

This week’s top game theory links: 5 August

Top game theory links from the past week: Wall Street Journal piece on gang colours, signals and evolutionary game theory: Why kamikaze behavior in bacteria is a good strategy: Commuter’s Game Theory: How to know when it’s your … Continue reading

Normal form games

There are two main ways in which games can be represented in game theory. One is the normal form (also called strategic form) and the other is the extensive form. This post will explain the normal form. In a normal … Continue reading

Don’t mess with a bald guy!

Yesterday’s post looked at the ultimatum game, where one player has some money and can offer some of that money to another player. If the other player rejects the offer then both players get nothing. Research by Terence C Burnham … Continue reading

When would you turn down free money?

People will turn down free money if they think the deal is unfair. The ultimatum game is a simple game which shows this. The first player is given £100. They then choose to give a proportion of that money to … Continue reading

This week’s top game theory links: 29th July

Here are my top five game theory links from the last week: 1 – The game theory of budget negotiations and debt ceiling (New York Times): 2 – Why are rival gas stations always across the street from one … Continue reading

Battle of the sexes: Barack and Michelle

In ‘The Battle of the Sexes’ game a man and a woman are trying to co-ordinate where they meet up one evening. In the usual version of the game the woman would rather go to the opera and the man … Continue reading

This week’s top game theory links

Here are my top five game theory links from the last week: What Game Theory and Neuroscience have to say about the US Debt crisis Bruce Bueno de Mesquita on game theory & forecasting: Lecture Notes on Game … Continue reading

Harry Potter, Lord Voldemort and game theory

Harry Potter could have used game theory to defeat Lord Voldemort. No-one dared to even speak the name of Lord Voldemort, only calling him ‘He-who-must-not-be-named’, ‘You-know-who’ or ‘the Dark Lord’. In Harry Potter and the Deathly Hallows anyone speaking his … Continue reading

Co-operation and trust

The stag hunt game is one of game theory’s classic games. In the game there are two cavemen going hunting for food, each one has two options: 1 –  go to where they know a stag has been spotted and … Continue reading

Obama and the $14 trillion debt ceiling

Barack Obama and Republican leaders are playing a game of chicken over the $14 trillion debt ceiling. None of them wants the US to default on its debts, but neither wants to be the one to back down. Whoever blinks … Continue reading

How to answer a question when you don’t even know the question!

Sometimes you can answer multiple-choice questions using game theory even if you don’t know the question! Imagine you are sitting an SAT test and the possible answers are: A. 5 – 2√6 B. 5 – √6 C. 1 – 2√6 … Continue reading

How Apple makes their supply chain more efficient

Apple’s developer contracts help to overcome supply chain inefficiencies and give Apple higher profits. Supply chains are inefficient if the wholesaler and retailer both try to maximize their profits independently, this was examined in yesterday’s post. Today will look at … Continue reading

Game theory and gamification are not the same thing

Adele Peters recently wrote a piece for with the headline ‘Weekend Reading: Using Game Theory to Make the World a Better Place’. Adele is clearly an intelligent woman as she works for the Haas School of Business, but the … Continue reading

What Amazon get right but American Apparel get wrong

Amazon uses focal points to help its customers use its website but American Apparel doesn’t. Yesterday’s post (here) talked about focal points helping your staff to make the right decisions. The same ideas can be applied to your customers. Products … Continue reading

Your business needs focal points to succeed

Thomas Schelling is a nobel prize winning economist who introduced the idea of focal points in 1960. A focal point is a strategy that players are likely to naturally choose. Schelling’s original example was two strangers trying to meet in … Continue reading

Nuclear war and credible threats

Each British nuclear submarine carries a letter from the British Prime Minister. It is kept locked away in a double safe, only to be opened if there is a nuclear war. Why is this done in an age of instant … Continue reading

When should you share your dessert?

Picture the scene: you are just getting to the end of a lovely, romantic dinner. You are looking through the dessert menu. Mmmm, chocolate cake, or maybe strawberry cheesecake? Then your partner says ‘I don’t want anything, but if you … Continue reading

What’s wrong with the Traveler’s Dilemma

The Traveler’s Dilemma is a problem in game theory that goes like this (from Wikipedia): An airline loses two suitcases belonging to two different travelers. Both suitcases happen to be identical and contain identical items. An airline manager tasked to … Continue reading

Game theory and Wimbledon

Wimbledon is now underway, so it is time to have a little think about how game theory might apply to tennis. Let’s assume that Roger Federer is playing Raphael Nadal in the final. And let’s say that Nadal is serving. … Continue reading

Introduction to game theory: Nash equilibrium

John Nash is the most famous game theorist, his life story was popularized in the book and movie A Beautiful Mind. The concept of a Nash equilibrium is also named after him. A Nash equilibrium is a situation where each … Continue reading

How to increase your lottery winnings

When choosing numbers for the lottery you can’t know which ones are going to win, but you can avoid sharing the prize with other players. Some numbers are selected more often than others and if you avoid these then you … Continue reading

Why better spam filters mean more spam

Are you fed up with the amount of spam e-mails that you receive? If you could have a spam filter that accurately blocked a higher percentage of spam then you would want it. But more accurate spam filters are not … Continue reading

Smart players sometimes lose to dumb ones

Sometimes you can be too clever for your own good. A well known game in game theory is one where the players are asked to choose a whole number between 0 and 100. The twist is that they have to … Continue reading

Why parking tickets are good for you

A town in west Wales has currently has no-one enforcing its parking rules. Aberystwyth used to have police run traffic patrols but these ended at the end of March. The local council is to take over responsibility for enforcing parking … Continue reading

Introduction to Game Theory: Common Knowledge

Common knowledge is a term used in game theory. A normal person would probably define ‘common knowledge’ as something that is known by everyone playing a game. Of course, a game theorist isn’t a normal person so they have a … Continue reading

Introduction to Game Theory: Prisoners’ Dilemma (Part 5)

The previous part in this series looked at what happens when a prisoners’ dilemma game is played multiple times. It turns out that the best strategy is ‘tit for tat’, where you start off co-operating and then copy the other … Continue reading

Why global warming isn’t a tragedy of the commons

Global warming is often cited as an example of ‘the tragedy of the commons’, where a resource is overused until there is none left. Even though people know that it will eventually run out they still overuse it. What is … Continue reading

Vince Cable plays chicken with the unions

Vince Cable, the UK government’ s Business Secretary, has warned the major unions not to take co-ordinated strike action otherwise the government will introduce tougher union laws. He is playing a game of chicken with the unions. In a game of … Continue reading

Tragedy of the commons

The ‘Tragedy of the Commons’ refers to a situation where a shared resource is overused by the people using it, even though they know that if they all overuse it then it will run out. Take an example of overfishing. … Continue reading

Game theory and gun control

I have seen game theory used in an argument for relaxing gun control. The argument goes something like this: If someone breaks into your home then they can either be armed or unarmed, you can also be either armed or … Continue reading

Introduction to Game Theory – Prisoners’ Dilemma (Part 4)

The first three parts of this post have introduced the Prisoners’ Dilemma (Part one), given some real examples (Part two), and looked at what happens in reality (Part three). Each of those posts has looked at a single game of … Continue reading

Iranian sanctions extended to Venezuela, but will they work?

The USA has imposed sanctions on Venezuela’s state oil company in retaliation for them trading with Iran (CNN story). These sanctions are unlikely to have any effect: research has shown that generally sanctions don’t work, why is this? If anything … Continue reading

Shell and first mover advantage

Royal Dutch Shell have announced that they are going to build a floating liquefied natural gas facility. This will be the largest floating structure ever built, six times the size of a big aircraft carrier and costing up to $15 … Continue reading

Introduction to Game Theory – Prisoners’ Dilemma (Part 3)

My two previous posts (here and here) have explained the prisoners’ dilemma and shown some real life examples. But is it really how people behave in real life? If everyone behaved logically then the only sensible choice in a prisoners’ … Continue reading

Introduction to Game Theory – Prisoners’ Dilemma (Part 2)

This is the second post on the Prisoners’ Dilemma, the first explained the basics of the problem and is here. One real example of a real Prisoners’ Dilemma is when two companies in a market are deciding how much to … Continue reading

When irrational behaviour is really rational

Game theory is sometimes criticised because people think that it doesn’t produce results that are applicable in the real world. This is often more to do with simplistic assumptions than issues with the models. It has recently been reported that … Continue reading

Introduction to Game Theory – Prisoners’ Dilemma (Part 1)

The prisoners’ dilemma is usually the first thing that people come across when they start to get interested in game theory. This post will give a (maths free) explanation of the idea. It is called the prisoners’ dilemma because the … Continue reading

British Airways strike action, a game theory example

British Airways cabin crew have taken strike action for 22 days in the last 18 months (BBC story), it now looks like the strike action is close to ending, but was there a better way to handle this? The problem … Continue reading