IB Docs (2) Team
Applying game theory
Game theory and the Nash equilibrium
The American economist John Nash is a central figure in the application of Game Theory in Economics. In 1994 he won the Nobel Prize in Economics for his PhD thesis which set out the definition and properties of the central concept of non-cooperative games – Nash equilibrium.
The prisoner’s dilemma is one of the best-known examples of a Nash equilibrium where two people are accused of committing a serious crime. This is an adapted version of the prisoner’s dilemma based on a school example. Two students, for example, have been accused of a serious breach of their school’s IT policy by playing online computer games on the school’s IT system. Both students are guilty of breaking the IT rule and are going to be interviewed by the school’s principal.
The different outcomes of their interview with the principal can be summarised as:
- If both students confess, they will each receive a two-hour detention.
- If one confesses and the other does not, the one who confesses receives a one-hour detention and the one who does not is suspended from school (assume the student who confesses implicates the other).
- If neither student confesses, they are both let-off because there is no conclusive evidence, they broke the IT rule (neither student knows there is no evidence.)
- The students are kept separate during the investigation and cannot collude.
The outcomes for each student can be set out in a matrix format:
The Nash equilibrium to this situation is for both students to confess to breaking the IT rule as the best (or least bad) outcome for them. If they lie there is a risk they could be suspended if the other student confesses and this would be a bad outcome for their school record. In a Nash equilibrium, each person in a decision-making situation like the prisoner’s dilemma makes the decision (games-out) what is best for them, based on what they think the other will do.
It is interesting to think about what might happen if the students could discuss their decision to confess or deny breaking the IT rule. The outcome from agreeing to deny breaking the rule looks like a good one, but what happens if one student suddenly decides to confess out of guilt?
An application of game theory: panic-buying
Whenever shortage situations arise in shops the news media often reports heavily on panic-buying as a problem facing consumers. This was the case in the Covid Pandemic where supermarkets ran short of essential items such as pasta, rice and bottled water. A few weeks ago the UK suffered from a shortage of petrol(gas) due to delivery driver shortages. Politicians claim there is ‘no need to panic-buy' because this will only make the situation worse.
This is how game theory and the Nash equilibrium can be used to possibly explain why people often choose to panic-buy. Consumer A is considering whether to panic-buy petrol or not after hearing a news report that petrol(gas) stations are running short of supply. Other consumers are facing the same decision. The outcomes of the decision to panic-buy or not panic-buy are set out in the table below.
The Nash equilibrium suggests consumers should panic-buy because on the balance of outcomes this seems to be the best decision for them to make. As long as individual A chooses to panic-buy they are most likely to get the petrol(gas) they need and if they do not panic by they may well miss out.
Questions
This is an example of how can game theory be applied to a pricing decision by two businesses in a non-collusive oligopoly market producing pasta in Italy. In this case, the two firms dominate the supply of pasta which they sell to retailers. Both firms are experiencing rising production costs and they are deciding whether to increase the price of the pasta they supply to retailers or not.
1. Explain why the Nash equilibrium position for both Firm X and Y is to increase the price of the pasta they sell.
The Nash equilibrium is for both firms to increase their prices because the risk of experiencing a large loss is greatest if they leave the price of the cement they sell unchanged.
2. Explain what might happen if Firm X and Y had a collusive agreement to fix the price and output of the pasta they sell.
If Firm X and Y colluded they could both decide to leave the price they charge the same. This would still lead to a loss for both companies but it would be a smaller loss than cutting price. They would, however, need to trust each other not to break the agreement and cut the price.
3. Examine the assumptions used in applying game theory in this situation.
The assumptions might include:
- There are only two firms in the market and no other producers of pasta have any influence over the price and output. It is possible other smaller pasta producers might influence the market and there may also be influence from overseas suppliers.
- The profit and loss figures in the matrix are based on forecasted values and these may well in inaccurate.
- The management of each firm in the market is predicted to make decisions based on maximising profits/minimising losses and there could be other factors influencing the decisions taken. For example, one firm might be reluctant to cut the price because it may make the pasta they sell seem lower quality and adversely affect the brand image of the business.
- The decision outcomes might change over time. The price elasticity of demand for pasta might increase in the long run which could turn initial losses into profits as revenues rise.
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