Game theory (HL only)

Introduction

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.

Enquiry question

What is game theory and why can it be used to explain the behaviour of firms in oligopoly.

Lesson time: 1 hour

Lesson objectives:

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.

Teacher notes:

1. Beginning activity - begin with the opening activities and allow 15 minutes for your classes to complete this. (15 minutes)

2. Processes - technical Vocabulary - the students can learn the key concepts through the notes, which should take 5 minutes to go through and discuss. 

3. Practise activities - included on the handout should take around 30 minutes.  These are short answer exercises.

4. Final reflection exercise - contains a relevant paper one style question on this topic that your students can look at and discuss.  This topic of course can be included on papers one and three of the examination and this page contains both types of questions to practise on.  This activity could also be set as a homework or classwork exercise. (10 minutes)

 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?

While the best choice is for both prisoners to deny the charge this would be a very risky strategy, one that might end up costing you 10 years in jail.  For that reason many pairs will both end up convicted of the more serious charge.

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

Activities

1. Watch the following short video from the film a beautiful mind and then complete the questions that follow.

Questions

(a) Explain in your own words how John Nash's game theory applied to their attempt to find a date in a bar?

Adam Smith believed that the interests of the group (society) were best served by each individual looking after their own interests.  By contrast the arguments put forward by John Nash state that instead group members should work together to maximise their own collective benefit.  His theory was that each of the men should agree, in advance, which woman they would attempt to approach, rather than have all of them competing for the attentions of just one beautiful woman.  A woman that at best only one could win the heart of.

(b) Provide examples of how this theory could be used to increase sales revenue in a business that you are familiar with?

  This theory could be used in the following situations:

  • oligopoly firms colluding on price to set artificially high prices (rather than engaging in a price war)
  • competing firms bidding for contracts and agreeing in advance which firm would pitch for which contract so that they each of them get something
  • potential job applicants at a job fair
  • a group of customers colluding to ensure that the collective price paid is lower than by outbidding each other - such as at an auction.

Activity 2

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.

Firms operating in an oligopoly can use game theory because they are all act interdependently in the decisions that they make.  In other words, before making a pricing or marketing decision the company must first consider the likely response of this action from their competitors.

Activity 3: Dominant strategies

Watch the following short video and then explain what game theorists mean by a 'dominant strategy'.

A strategy is dominant if, regardless of what the other firms in the competing market do, this strategy earns the player (firm) a greater benefit than any other strategy.  So a dominant strategy is one that is always better than any other strategy, for any profile of other players' actions.  If one firm has a strategy which is dominant, than all others are dominated.  So in the video, firm A has the dominant strategy because it is always more profitable to advertise than not.  Similarly firm X should always lower their price, regardless of firm Y does.

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?

Each being 25% from the edge of the beach, so that both covers exactly 50% of the beach.

(b) Why are both ice cream vendors encouraged to cheat, rather than stick to the original agreement?

While the socially optimum placement provides each vendor with exactly 50% of the beach to serve, the lure of additional profit encourages both parties to cheat by stealing area from their competitor.

(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?

While the socially optimum level would appear to make sense, neither business entirely trusts the other and so by setting up next to each other, both businesses technically still control 50% of the beach and both can keep an eye on the other to prevent them from cheating on their deal.

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?

Activity 6: Link to the assessment

Examples of paper one questions include:

Part (a)

Explain why firms operating in an oligopoly might wish to collude.  [10 marks]

Command term: Explain

Key term to define: Oligopoly

When a small number of firms dominate an industry the goods or services sold will be substitutes for each other, either close substitutes in the case of the petrol or sugar industry or weaker substitutes, such as the smart phone market, where Apple and Samsung compete in the same market but with slightly differentiated products.

In the case of a a price war or an arms race where each business spends increasingly large sums of money on either marketing or product development, neither business is likely to benefit.  This makes the case for collusion compelling.  Collusion can be either official in the form of a cartel such as OPEC or an unofficial / tacit agreement between rival businesses.

Collusion is relatively easy in oligopolistic markets because of the small number of businesses involved.

Part (b)

Using real world examples, discuss the view that governments should always act to prevent the creation of monopolies.  [15 marks]

Command term: Discuss

Key term to define: Monopoly

Real life examples might include situations where governments have successfully prevented the formation of a monopoly, e.g. the UK governments decision to refuse permission for the merger of THREE and O2 or attempts by the USA government to restrict monopolies, such as the acquisition of T-Mobile by AT&T.   Responses should also include markets where the government has failed to prevent the formation of a monopoly such as with social media outlets such as Facebook, Twitter e.t.c. 

The command term discuss requires a response which considers both sides of the argument.  There are a number of economists who support the view that monopolies will always act in their own self interest, to the detrement of the consumer.  Others argue that in certain cases the formation of a monopoly can bring benefits to the consumer in the form of lower prices and greater choice.  This is because in some markets the potential gains from economies of scale can mean large sums invested in product development as well as lower costs / prices.

Recent examples of both include Amazon's purchase of Whole Foods, which the US government considered to be in the public interest as well as the merger of Three and O2, which the UK government blocked stating that the new business was likely to act against the public interest.  In this example the UK regulator dismissed the companies argument that the new company would provide benefits to the consumer from increased returns to scale.

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