Oligopoly and Game Theory

In brief, game theory is about making predictions about another person's actions. In this chapter we provide an introduction to game theory and consider some areas where lessons from game theory can be applied by economist from climate change negotiations to the incentives to engage in crime!

The Monty Hall problem!

Suppose you‟re on a game show, and you‟re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say number 1, and the host, who knows what‟s behind the doors, opens another door, say number 3, which has a goat. He says to you, “Do you want to pick door number 2?” Is it to your advantage to switch your choice of doors? Possible answer to the Monty Hall problem

Game Theory

Game theory is mainly concerned with predicting the outcome of games of strategy in which the participants (for example two or more businesses competing in a market) have incomplete information about the others' intentions. Game theory analysis has direct relevance to the study of the conduct and behaviour of firms in oligopolistic markets – for example the decisions that firms must take over pricing, and how much money to invest in research and development spending. Costly research projects represent a risk for any business – but if one firm invests in R&D, can a rival firm decide not to follow? They might lose the competitive edge in the market and suffer a long term decline in market share and profitability. The dominant strategy for both firms is probably to go ahead with R&D spending. If they do not and the other firm does, then their profits fall and they lose market share. However, there are only a limited number of patents available to be won and if all of the leading firms in a market spend heavily on R&D, this may ultimately yield a lower total rate of return than if only one firm opts to proceed. The Prisoners’ Dilemma

The classic example of game theory is the Prisoners‟ Dilemma, a situation where two prisoners are being questioned over their guilt or innocence of a crime. They have a simple choice, either to confess to the crime (thereby implicating their accomplice) and accept the consequences, or to deny all involvement and hope that their partner does likewise. Confess or keep quiet? The Prisoner’s Dilemma is a classic example of basic game theory in action!

The “pay-off” is measured in terms of years in prison arising from their choices and this is summarised in the table below. No communication is permitted between the two suspects – in other words, each must make an independent decision, but clearly they will take into account the likely behaviour of the other when under interrogation.

“When I am getting ready to reason with a man I spend one-third of my time thinking about myself and what I am going to say, and two-thirds thinking about him and what he is going to say.”

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Source: Abraham Lincoln

Here is an example of the Prisoners‟ Dilemma:

Prisoner A Two prisoners are held in a separate room and cannot communicate They are both suspected of a crime They can either confess or they can deny the crime Payoffs shown in the matrix are years in prison from their chosen course of action

Confess Deny Confess (3 years, 3 years) (1 year, 10 years) Prisoner B Deny (10 years, 1 year) (2 years, 2 years)

What is the best strategy for each prisoner? Equilibrium happens when each player takes decisions which maximise the outcome for them given the actions of the other player in the game. In our example of the Prisoners‟ Dilemma, the dominant strategy for each player is to confess since this is a course of action likely to minimise the average number of years they might expect to remain in prison. But if both prisoners choose to confess, their “pay-off” i.e. 3 years each in prison is higher than if they both choose to deny any involvement in the crime. That said, even if both prisoners chose to deny the crime (and indeed could communicate to agree this course of action), then each prisoner has an incentive to cheat on any agreement and confess, thereby reducing their own spell in custody.

The equilibrium in the Prisoners‟ Dilemma occurs when each player takes the best Prisoner A possible action for themselves given the action of the other player.

The dominant strategy is each prisoners‟ unique best strategy regardless of the other players’ action Best strategy? Confess?

A bad outcome! – Both prisoners could do better by both denying – but once collusion sets in, each prisoner has an incentive to cheat! Confess Deny Confess (3 years, 3 years) (1 year, 10 years) Prisoner B Deny (10 years, 1 year) (2 years, 2 years)

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Applying the Prisoner’s Dilemma to business decisions

Game theory examples usually revolve around the pay-offs that come from making different decisions. One arrangement of possible payoffs is as follows: T refers to the temptation to defect

R refers to the reward for mutual cooperation between players P refers to the punishment for mutual defection S refers to the sucker‟s payoff In the classic prisoner‟s dilemma the reward to defecting is greater than mutual cooperation which itself brings a higher reward than mutual defection which itself is better than the sucker‟s pay-off. And critically, the reward for two players cooperating with each other is higher than the average reward from defection and the sucker‟s pay-off. Consider this example of a simple pricing game: The values in the table refer to the profits that flow from making a particular decision.

Firm B’s output

High output Low output High output £5m, £5m £12m, £4m Firm A’s output Low output £4m, £12m £10m, £10m Display of payoffs: row first, column second e.g. if Firm A chooses a high output and Firm B opts for a low output, Firm A wins £12m and Firm B wins £4m. In this game the reward to both firms choosing to limit supply and thereby keep the price relatively high is that they each earn £10m. But choosing to defect from this strategy and increase output can cause a rise in market supply, lower prices and lower profits - £5m each if both choose to do so. A dominant strategy is a strategy that is best irrespective of the other player‟s choice. In this case the dominant strategy is competition between the firms. Game theory analysis has direct relevance to our study of the behaviour of businesses in oligopolistic markets – for example the decisions that firms must take over pricing of products, and also how much money to invest in research and development. Costly research projects represent a risk for any business – but if one firm invests in R&D, can another rival firm decide not to follow? They might lose the competitive edge in the market and suffer a decline in market share and profitability. The dominant strategy for both firms is probably to go ahead with R&D spending. However, there are only a limited number of patents available to be won and if all of the leading firms in a market spend heavily on R&D, this may ultimately yield a lower total rate of return than if only one firm opts to proceed. The Prisoners’ Dilemma can help to explain the break down of price-fixing agreements between producers which can lead to the out-break of price wars among suppliers, the break- down of other joint ventures between producers and also the collapse of free-trade agreements between countries when one or more countries decides that protectionist strategies are in their own best interest. The key point is that game theory provides an insight into the interdependent decision- making that lies at the heart of the interaction between businesses in a competitive market.

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Case Study: Claims of Price Rigging in the Food Industry

There is plenty for the consumer to feel irked about as the cost of food, petrol and other essential basics seems to race ahead of the general rate of inflation. Yet now it seems there is a conspiracy among some large companies to fix the price of other goods we buy, such as toothpaste and shampoo.

There is currently an OFT investigation into the pricing behaviour of some big name companies - Proctor and Gamble, Coca- Cola, Kimberly-Clark, GlaxoSmithKline and Unilever. The leading supermarkets – Tesco, Sainsbury, Asda and Morrisons have also received visits by OFT investigators. What these large companies have in common is that economists would classify them as oligopolies (industries where there are a small number of large firms). These businesses can behave in the following ways as economic theory predicts:

Prices are sticky – by expecting the worst, firms are most likely to choose non-price competition. If a firm is considering a price rise, the worst outcome would be if the other firms in the industry do not increase their prices, causing the firm to lose business. Therefore the firm will be reluctant to raise prices. If a firm is considering reducing its price, the worst outcome is if all the other firms also choose to cut prices. The firm will not gain market share, but will end up with less revenue. Therefore the firm will be reluctant to decrease its price, all other things being equal. So firms will, instead, use methods of non-price competition such as „buy one, get one free‟, „3 for 2‟ offers, free gifts, loyalty points, etc. Firms are likely to spend large amounts on advertising designed to establish brand loyalty.

Price wars – sometimes an oligopoly will make an aggressive move to try and win market share. The big name supermarkets do this from time to time. One firm cuts prices significantly and others follow or undercut so as not to lose their share. This can be a good outcome for consumers, but does not appear to be happening at present.

Collusion – this is where the firms choose to act together to „fix‟ prices and can be illegal. However, some collusive behaviour is hard to pin down, which is why an OFT investigation is going ahead. If costs of production increase, it is not unreasonable to expect all firms in the industry to respond with an increase in price, but there appears to be some evidence, for example, that supermarkets have used rising costs as an excuse to inflate their prices to increase profit margins. If it does transpire that some of the best known companies have been acting illegally by price fixing, this will look very bad for them at a time when consumers are already feeling the pinch. Source: Liz Veal, EconoMax, June 2008

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Case Study: Prisoner's Dilemma and Climate Change Negotiations

Can repeated games of the prisoner‟s dilemma help climate negotiations? With 2012 signalling the expiry date of the Kyoto Protocol, there is an urgent need for a successor treaty to tackle the ever-increasing global emissions problem. The main issue with tackling climate change is the cost to countries of implementing it. To be successful it will need profound transformation of energy and transport organisations, and changes in the behaviours of billions of consumers. The Stern Review admitted that it will likely cost 1% of GDP – even though it doesn‟t seem much, it is double the amount currently spent on development aid worldwide.

The USA sees a cap on carbon emissions as a threat to competitiveness, and hence to its global supremacy;

The developing world denounces any calls for a cap on emissions as an effort by former colonial powers to hold back development;

Europe has been making encouraging though patchy progress towards targets, driven mainly by a one-off switch from coal to gas. The issue here is how countries can expect to make cuts in emissions when their economic competitors refuse. This in turn leads to the Tragedy of the Commons which occurs when a group‟s individual incentive lead them to take actions which, overall, lead to negative consequences for all group members. A country that refuses to act, whilst the other cooperates, will experience a free-rider benefit - enjoying the advantage of limited climate change without the cost. On the flip side, any country that imposes limits, when its competitors do not, incurs not just the cost of limiting its own emissions, but also a further cost in terms of reduced competitiveness The dynamics of the prisoner‟s dilemma do change if participants know that they will be playing the game more than once. In 1984 an American political scientist at the University of Michigan, Robert Axelrod, argued that if you play the game repeatedly you are likely to see emerging is cooperative rather than defective actions. He identified four elements to a successful strategy which is this case can be applied to climate negotiations: 1. Be Nice – sign up to unilateral cuts in emissions, as deep as your economy and financing capacity allows. 2. Be Retaliatory – single out countries that have not commenced action and, in collaboration, find ways of pressurising them until they do so. 3. Be Forgiving - when non-compliant countries come onboard give them generous applause; signal that good behaviour will be rewarded with even deeper cuts in your own emissions. 4. Be Clear - let everyone know in advance exactly how you are going to behave – that you will work with them if they take action on emissions, and that you will retaliate if they do not. Repeated Prisoner‟s Dilemma provides valuable insight into how countries should act away from the negotiating table and over the longer term. Ultimately, for the planet‟s sake, one hopes that everyone will play the game

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Source: Mark Johnston, EconoMax, December 2007

John Maynard Keynes’ “The Beauty Contest”:

“...professional investment may be likened to those newspaper competitions in which the competitors have to pick out the six prettiest faces from a hundred photographs, the prize being awarded to the competitor whose choice most nearly corresponds to the average preferences of the competitors as a whole; so that each competitor has to pick, not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view. It is not a case of choosing those which, to the best of one‟s judgment, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be.” Source: J.M. Keynes; General Theory, p.156, 1936

Suggestions for further reading on game theory Game theory resources (US based site) www.gametheory.net/

Game theory society (US based site) www.gametheorysociety.org/ Prisoners Dilemma and a Big Brother Housemates Game! http://www.paulspages.co.uk/hmd/ Do economists need brains? (The Economist, July 2008) Game of co-operation and betrayal Game theory and the Dark Knight (Pure Pedantry Blog, July 2008)

Game theory could save the world (Telegraph, July 2008) Reaping rewards for cheating (Sydney Morning Herald, July 2008) Supermarket petrol price cuts (BBC news, July 2008)

Under the hammer – auctions and game theory (Tim Harford, May 2007) World Cup Game Theory (Tim Harford, Slate, July 2006) World trade talks collapse over tariff protection (Guardian, July 2008)

Suggestions for further reading on oligopoly

Call to investigate energy 'oligopolies' (Guardian, May 2008) Collapse of the DOHA trade negotiations – free trade versus protectionism (BBC news, July 2008) Comfortable power oligopoly ripping off customers (The Times, May 2008) OPEC cartel‟s empty tool kit (Fortune Magazine, July 2008) Tescopoly website Thai cartel idea outrages rice consumers (Times, May 2008) Top Paris hotels guilty of price fixing (Times, November 2005) Wake up to old-fashioned power of new oligopolies (Financial Times, February 2006)

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