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Game theory is used to by mathematicians to calculate the best course of action to take in various strategic situations. At its most complex game theory can be used, not only by businesses and economists, but also social scientists, psychologists, philosophers and biologists. At its simplest, it’s something we can all make use of in our everyday lives.<\/p>\n
Whilst game theory has many different forms depending on the situation it is applied to, it is easiest to explain by giving a basic example of how it works, such as the well known prisoner’s dilemma;<\/p>\n
Imagine that you and a friend have been arrested by the police force of a corrupt government, accused of a joint crime. They are assuming that you are guilty and there will be no trial. Instead, they offer you two options; deny the charges or confess to them.<\/p>\n
The possible outcomes of your decision are;<\/p>\n
You are held in separate cells and can’t communicate.<\/p>\n
The situation and its possible outcomes can be expressed in a matrix like this;<\/p>\n
<\/p>\n
If you think they will deny, it is best to confess. That way you go free instead of getting 5 years for denying it along with them.<\/p>\n
However, even if you think they will confess, it is still better for you to confess as well. That way you’ll only get 10 years, avoiding the 20 years you’d get if you choose to deny the charge.<\/p>\n
As, no matter what the other person does, it is better for you to confess, confession is what’s called the ‘dominant’ strategy.<\/p>\n
So, with that in mind maybe it’s not a dilemma at all? Surely it is best just to confess, isn’t it?<\/p>\n
This situation is what’s called a ‘Nash equilibrium’ (named after the pioneering mathematician John Nash, played by Russell Crowe in the film ‘A Beautiful Mind’).<\/p>\n
In a ‘Nash equilibrium’ one person looks at what the other might do and decides that, as they can’t tell what their choice will be, they have to stick with the option that is safest in all cases. They have to go for the ‘dominant’ strategy. This applies to both prisoners, hence the state of equilibrium.<\/p>\n
But is this actually what’s best for the people involved? No, it isn’t!<\/p>\n
Why? Look again at the prisoner’s dilemma example above. Because both prisoners will reach that same conclusion that confession is the ‘dominant strategy’ both will confess. That means they both get 10 years in jail.<\/p>\n
However, if they both deny they only get 5 years! This is the option that involves the least combined jail time. On top of that the jail time is split fairly between both parties. This makes it what’s called the ‘optimum outcome’. In other words, it’s the best thing that could happen, overall.<\/p>\n
But can you trust your partner to figure this out? If you deny and they still confess you’re looking at 20 years!<\/p>\n
In real life people, especially when it comes to businesses, tend to see others as competition rather than partners. Therefore, they go for the safe option i.e. the dominant strategy.<\/p>\n
The real lesson of ‘Nash equilibrium’ is that, due to not cooperating properly people and businesses usually miss out on the ‘optimum outcome’ because they are scared of straying from the ‘dominant’ option, which guards against the unpredictability of others.<\/p>\n
Basically, we could all be better off if we all worked together, but in business that isn’t how it works.<\/p>\n
The way that businesses decide on their pricing structures is very similar to the logic of the prisoner’s dilemma.<\/p>\n
When a business sets a pricing strategy it has two basic options;<\/p>\n
These are the two extremes of the scale and all pricing strategies fall between these two poles. But if this is the case, why do similar products generally cost more or less the same? Why don\u2019t we see a wider variety of pricing structures used?<\/p>\n
The answer lies with the Nash Equilibrium.<\/p>\n
In our earlier example we saw that if each prisoner denied the charge it would produce the ‘optimum outcome’ but that they would also run the risk of going down for 20 years if their partner confessed.<\/p>\n
For two similar competing businesses the optimum outcome would be if they both set high prices, as they would make high profits on each sale and, as customers would have little reason to pick one over the other, prices being the same, they would likely have an equal market share.<\/p>\n
However, if one business sets its prices at an artificially high level, they have no guarantee that other businesses will do the same. They run the risk of competitors undercutting them.<\/p>\n
Should this happen the business with the lower price will take a huge chunk of the market share, as customers will choose the cheaper option. The firm with lower prices will prosper and the firm with high prices will be ruined.<\/p>\n
By this logic, if one firm finds itself in a position where it can offer extremely low prices, all the other firms are forced to lower theirs as well, to avoid losing custom. This will eat into their profits and make all the businesses worse off.<\/p>\n