game theory

Game Theory

A model of optimality taking into consideration not only benefits less costs, but also the interaction between participants.

Investopedia Commentary

Game theory attempts to look at the relationships between participants in a particular model and predict their optimal decisions. One frequently cited example of game theory is the prisoner's dilemma.

Suppose there are two brokers accused of fraudulent trading activities: Dave and Henry. Both Dave and Henry are being interrogated separately and do not know what the other is saying. Both brokers want to minimize the amount of time spent in jail and here lies the dilemma. The sentences vary as follows:

1) If Dave pleads not guilty and Henry confesses, Henry will receive the minimum sentence of one year, and Dave will have to stay in jail for the maximum sentence of five years.
2) If nobody makes any implications they will both receive a sentence of two years.
3) If both decide to plead guilty and implicate their partner, they will both receive a sentence of three years.
4) If Henry pleads not guilty and Dave confesses, Dave will receive the minimum sentence of one year, and Henry will have to stay in jail for the maximum five years.

Obviously, pleading guilty is the most attractive should the other plead not guilty since the sentence is only one year. However, if the other party also chooses to plead guilty, both will have to serve three years. On the other hand, if both parties plead not guilty, they'd have to serve two years in jail. Consequently, the risk of pleading not guilty is a five-year sentence, should the other choose to confess.

The prisoner's dilemma described above is illustrated in the following diagram:

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See also: Behavioral Finance, Dismal Science, Economics, Zero-Sum Game