Game theory (HL only)
This lesson focuses on game theory, which many of your students will know from the film 'a beautiful mind' starring Russell Crowe as John Nash. In the film John Nash created the economic concept known as the prisoners dilemma. The prisoner's dilemma is used to predict likely human behaviour and is used in the study of bargaining, auctions, oligopoly markets, mergers and pricing.
This lesson includes a scene from that film and captures the moment when it is claimed that economist John Nash first devised the idea that free market economics may not always work and that by working together firms could benefit more than by simply looking after their own interests, as described by Adam Smith.
What is game theory and why can it be used to explain the behaviour of firms in oligopoly.
Lesson time: 1 hour
Explain how game theory (the simple prisoner’s dilemma) can illustrate strategic interdependence and the options available to oligopolies.
Explain the incentive of cartel members to cheat. Examine the conditions that make cartel structures difficult to maintain.
Opening activity: The prisoner's dilemma
Divide the class into pairs and ensure that they cannot speak to each other or communicate in any other way, for example by signalling across the room to each other. Then in pairs describe the dilemma to them. You suspect they have committed a crime worthy of a 10 year sentence and that you also have sufficient evidence to support a lesser charge which would mean 2 years in jail. Each prisoner is given the choice of either confessing to the crime, which means implementing their friend or denying everything, in which case they would serve two years for the lesser crime.
Their choices are as follows:
1. Confess to the serious charge, in which case the Police will let them go and their friend then serves 10 years in jail. However, this presumes that their friend chooses to play ball and deny the charge. If in turn the friend confesses then both will serve 5 years in jail.
2. Deny the charge, in which case they and their friend will still do 2 years in jail for the lesser charge - presuming that the friend also denies the charge. Denying the charge runs the risk of their friend confessing, in which case they will go to jail for 10 years with the friend going free.
Which decision will you choose, confess or deny?
The prisoner’s dilemma in practise
The prisoners dilemma works in practise in the Turkish ski resort of Erzurum, a small city but with world class skiing. There are 5 hotels within the ski resort, one of which is featured in the diagram to the right. All offer an all inclusive package of accommodation, a daily ski pass, food and even locally produced alcohol to drink.
Residents and sometimes even tourists will shop around for the best deals before making their purchase. In this example the hotels are the 5 prisoners waiting to be interrogated. If they all collude together, they can each charge the same (presumably high price) and each hotel would benefit at the expense of the customer. To this end each has an official price for the packages. However times are currently difficult within the skiing industry in Turkey. With many tourists staying away the few remaining customers are more aware of their strong bargaining position and can now shop around with greater freedom than before.
So what do the hotels do in this scenario? Stick to their initial agreement and maintain high prices for all? Or do they offer discounts to customers in the knowledge that the rival hotels may also cut their prices?
The handout including the activities is included as a PDF file at: Prisoners dilemma
1. Watch the following short video from the film a beautiful mind and then complete the questions that follow.
(a) Explain in your own words how John Nash's game theory applied to their attempt to find a date in a bar?
(b) Provide examples of how this theory could be used to increase sales revenue in a business that you are familiar with?
Watch the following video which explains game theory through the movie 'the dark knight' and then provide your own example of an oligopoly market which also uses the theory in its pricing and marketing decisions.
Activity 3: Dominant strategies
Watch the following short video and then explain what game theorists mean by a 'dominant strategy'.
Activity 4: Why are competing firms incentivised to cheat
Watch the following video and then answer the following questions:
(a) What do game theorists believe is the socially optimum level of placement for the two competing ice cream firms?
(b) Why are both ice cream vendors encouraged to cheat, rather than stick to the original agreement?
(c) Use your answers from (a) and (b) to explain why many businesses set up next to each other, ignoring the socially optimum placement level?
Activity 5: Applying the prisoners dilemma to the classroom
Watch the following short video and see students battle to score points towards their GPA. How would your classes do in this experiment?