Game Theory in Business Applications

Nash equilibrium Now that we have realized that we have to move in a somewhat similar direction to the economists, maybe we should consult the experts of the game theory at this point.

In the 1980's Axelrod and Hamilton worked on a famous problem in the game heory, the Prisoner's Dilemma, exactly because it deals with this problem. The rational pursuit of individual self-interest drives everybody into an outcome that is not favored by anybody. Imagine two partners in a crime being interrogated at the same time.

Each one has two options, cooperate with the other and keep quiet or betray the other and confess.

Case C, we can say, is if both cooperate then the police cannot get much out of them and they will both get a light sentence (2 years); if one defects and the other keeps quiet then the traitor will get an even lighter sentence (1 ear) - this is case B. If the one who cooperates gets the longest sentence (10 years), this is the worst end of the deal and we can call this case S.

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In a case when both betray one another they will both get a sentence (6 years) longer than if they had cooperated but lighter than if one had kept quiet and the other spoke, and this is case D.

Out of the four outcomes, B is the best and S is the worst from an individualistic point of view, while the order of preference is B, C, S, D. We should realize that this is a non-zero sum game.

In a zero-sum game, my loss is your gain; for example, if we re trying to divide a certain amount of money in the bank into two, anything over fifty percent for me is a loss for you. On the other hand, in a non-zero sum game I can actually win without you losing.

Each suspect has to make their decision without knowing what the other has done. What would a rational suspect do? The answer is simple; he would betray his partner in crime! Regardless of what the other suspect does, betrayal always pays better than cooperating. Here is the simple reasoning one would follow. Suppose my partner in crime cooperates. I could do quite well by also cooperating, I would get 2 years, (C). But it is even better to betray him, since I would then get 1 year instead of 2, (B).

What if he betrays me? If I keep quiet then the worst is going to happen and I will get 10 years, (S), therefore I should defect and get 6 years, (D). In summary, all we are saying is that the second row in the chart is always more favorable than the first row, hence no matter what, a rational prisoner would always betray his partner! "And here comes the dilemma: it pays each of them to defect, whatever the other one does, yet if both defect, each does less well than if both had cooperated.

What is best or each individual leads to a mutual defection, while everybody would be better off Fortunately, the dilemma has a solution in our case. So far, we have only played the game once. What happens if the parties play the game repeatedly and for an indefinite number of times? After every single time they play they know that they are likely to meet again later. Under such conditions there is actually a cooperative strategy for the players that could be successful; this is a somewhat twisted version of the cooperation defined earlier in the prisoner's dilemma case.

First of all, we mmediately realize that always defecting is clearly not the smartest strategy, knowing that you will meet the other individual again in the future. Instead, consider this natural strategy, called Tit for Tat, which is never to be the first to defect, always imitate the other from his previous move and retaliate only when you have been betrayed. It turns out that this highly cooperative strategy can survive, even though initially it withstands the challenges of readily defecting strategies. And it can be stable against diminishing altogether.

In order for this Tit for Tat strategy to have a chance to work, a critical proportion of he individuals have to cooperate. Otherwise the readily defective strategies would simply destroy the cooperative ones and dominate the whole system. But once the number of individuals who adopt a Tit for Tat strategy exceeds a critical ratio in the population then it survives and reaches a stable ratio able to withstand any other strategy. Axelrod's theory is nice and easy to understand, but once again it prompts all sorts of other issues.

How frequently the population is able to reach that critical level in the first place? On the other hand, what kind of a memory do individuals need in order to e able to execute a Tit for Tat strategy? What do we make of it? We could keep working on expanding these explanations and models, or at least the biologists should. But in any case, in order for any of these models to apply in what we see in nature we have to be demanding of the individuals who form the population.

Every single time we come up with a new approach or an extended model it is difficult to explain many of the characteristics of altruistic behavior, even in idealized cases. Either there must be altruistic genes that can recognize the other altruistic genes carried in other individuals, or we all individuals have a well- eveloped memory that actually remembers all the moves that have been made by other individuals in the population, or one starts from an idealistic state in order to maintain the stability of the system without knowing how we are able to get there in the first place.

It seems that the smarter we get, the better our theories are developed, and the more flawless our models become, the more we realize that all the individuals in the great ecosystem of nature that show some kind of altruistic behavior must have a great about the whole picture and they must have an authority that has a great impact on others, on and on and on.