Game Theory
n this small essay, the problem of co-operation in business relationships and some solutions will be discussed using game theory. There are some different kinds of business relationships. However, the relationship between the firm and its competitors will be mainly investigated instead of covering all of them 1. The reason is that it is easy to adapt to other ones.
Let's start by considering a famous story to understand the problem of co-operation in business. The story's called Prisoner's Dilemma.
John and Peter have been arrested for robbing the bank and placed in separate isolation cells. The police do not have sufficient evidence to convict them unless one of them confesses. If neither confesses, they are convicted of a minor crime and are sentenced to 2 months. If both confess, they spend 12 months in jail. However, if one confesses and the other does not, the confessor is released immediately but the other is sentenced to 18 months in jail - 12 for the crime and 6 for obstructing justice.
Peter (deny) Peter (confess)
John (deny) 2, 2 18, 0
John (confess) 0, 18 12, 12 NE
(NE - Nash Equilibrium 2)
With self-interest, both have incentive to confess. For example, to John, if Peter denies, John will be free immediately, otherwise his time in jail will be reduced from 18 months to 12 months. So it is better for John to confess no matter what Peter does. We call confessing dominant strategy which gives you a better payoff irrespective of what your opponent does. The situation is the same with Peter. The result is that both confess and both will be in jail for 12 months. However, they could be better-off if both deny. But as I will show, it is difficult to achieve this better outcome. The essential reason is the contradiction between self-interest and common-interest. It is very risky for John (or Peter) to deny because his opponent has strong incentive to confess.
As you can see from Prisoner's Dilemma, co-operation is not always easy...
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