The Prisoner’s Dilemma,

Game theory tries to offer a mechanism to solve problems of strategic interaction. This is when your benefit depends not only on your own choices but equally on those of others around you. Strategic interaction is fundamental to economics, whether one firm decides to compete or cooperate with another in a market place is just one of many examples. Such an example on a macro scale could be for the product of oil. OPEC (one of the most famous swing producers) shows us that cooperation in a market place can be incredibly successful however, of course, we know that competition can be very important for a market economy. It is competition that keeps industries efficient, trying to cut down costs and striving for a more competitive production line. It was the large amounts of competition and laissez faire (do nothing) governmental approach in the industrial revolution that led to numerous important technological inventions. This competitiveness can reduce the risk of inflation, reduce the significance of a social hierarchy and improve the standard of living for the majority. These two choices, to compete or cooperate in an economy are very important.

When two companies or a group of companies supplying the same product have informally agreed to set a minimum price for the market place there poses a great dilemma. This situation can be expressed by the graph on the right hand side. The market price, or what the price should be, is at 'P' on the graph however the informally agreed price is at 'Pm'. If we look from a single company’s prospective we see two options, cooperation or competition. Cooperation being to agree to the informal price and keep to the informal agreement while the latter, to compete is to go against the terms previously agreed and lower your prices below 'Pm'. This will suddenly increase your demand in the very short term as your prices will be lower than your competitors and therefore all of those interested in buying the product each of you both supply, will choose to buy from the company that lowered their prices instead.

Hypothetically speaking, let’s assume this group of companies only contains two companies and that these two companies have arranged the minimum pricing agreement before, and in full knowledge of, a nearby long term oil contract with the US. The oil contract being for an up and coming war, which due to scarce resources and sudden great demand puts them in a weak bargaining position (making them vulnerable to lose their consumer surplus).

Now, with this information, the dilemma really starts to be of great importance. You and ‘company 2’ have agreed to share the contract profit received equally (with each of you equally contributing to the oil supply as well). The options and payoffs from this contact of one company, your company are as follows:

(assuming that the contact is predicted to have a £25 mil profit margin when demanded by you and company 2 with the agreed minimum price. Also you and company 2 being the two only oil suppliers in the market).

Company 2:       Your Decisions:	Cooperate	Compete
Cooperate	(£12.5mil), (£12.5mil)	(£0), (£20mil)
Compete	(£20mil), (£0)	(£5mil),(£5mil)

The top row represents your decisions which correlates to the 2^nd payoff in brackets. Company 2’s payoffs are listed first and are represented by the far left column.

Lets look at the options, option one, choosing to cooperate has 2 possibilities. Firstly both of you follow this same line of logic and both cooperate. This allows the greatest total profit to be obtained and shared equally. The second outcome is that your opponent competes without your knowledge, they then lower their profit margins to let’s say £20mil making themselves more competitive and secure the contract. You therefore get nothing. When you choose to compete, the same option applies to you when your opponent chooses to cooperate, blindly ignorant of your deceitful ways.  Lastly there is the option that both of you compete, each trying to gain the advantage, then the price is determined by how low each of you compete with each other to secure the contract. As you both are competing against each other after agreeing £12.5mil profit margin each, cooperating again is very unlikely so the likely price is to be less than £12.5mil, let’s say £10mil profit for the overall contract. Due to ease of modelling, let’s say that the US agrees a £5mil contract with both you and the other company securing the same quantity of oil supplied. With these possible outcomes comes the basis of prisoner’s dilemma and its application in economics.

Now, imagine you are considering company two’s decisions. If they cooperate then you can obtain £12.5mil by equally cooperating or £20mil by competing. So you compete, it’s only logical! You gain £7.5mil greater profit. So now imagine that company two decides to compete, if you cooperate you get nothing but company 2 gets everything. If you compete too you at least get £5mil, so you compete again. Competing is a dominant strategy for you and as company 2 is in the same situation it is only logical that they will conclude the same thing. Just ask what would the other player do, and what is the best response to this. But wait, competing is the best strategy? 

Let’s have a look at this:

Company 2:       Your Decisions:	Cooperate	Compete
Cooperate	(£12.5mil), (£12.5mil)	(£0), (£20mil)
Compete	(£20mil), (£0)	(£5mil),(£5mil)

The cells/ areas with a blue border represent Company 2’s dominant strategy (to compete). The green filled cells/ areas represent your dominant strategy (again to compete). Therefore the bottom right side cell is the logical outcome, neither you nor company two can change your/their choice and set to gain an advantage (assuming that the other stays with the original choice to compete). There is no unilateral incentive for either of you to change from the original strategy. This is what is known as a Nash equilibrium. So, Nash’s equilibrium tells us that the ideal solution, or rather rational solution is for both of you to compete and gain £5mil each but wait, is this really the case? If both cooperate you both gain £7.5mil greater than if you both compete, so is this the rational solution at all? This is a major flaw in Nash’s equilibrium and is an argument against game theory. Other arguments include that people aren't rational (emphasized in the Flood-Dresher experiment). On moves 83 through to 98 both player cooperated in the Flood Dresher experiment which was a simple game to demonstrate the prisoner’s dilemma. Both players therefore reaped the greatest benefits however this took at total of 82 turns before they began to sustainably cooperate. In our situation we have only one turn and a contract of this significance is unlikely to come along anytime soon, so we can’t learn our ‘opponent’s’, ‘company 2’s’ strategy. The late 1950’s Ohio state studies at Ohio State University which followed a similar game to demonstrate the prisoner’s dilemma showed that most participants chose to ‘compete’ or ‘defect’ most of the time, following the dominant strategy and yet if they cooperated a greater benefit could be achieved between them. The sum of cooperation pay outs is greater than the sum of any other scenario in the table however it seems fundamentally human nature to defect in aspiration of obtaining a greater amount of wealth than your opponent. Perhaps its evolutionary or instinctive to compete rather than cooperate, it’s human nature, or perhaps there is another explanation.

As one of the great unsolved dilemmas of game theory, the prisoner’s dilemma still poses a great flaw in it's very fundamental fabric of application and equally creates great questions about the very nature of human beings and whether we are truly rational creatures. So, ask yourself, what would you do?