Non-Zero-Sum Games

Non-zero-sum games, on the other hand, are those that potentially have net results other than

zero. This simply means that the loss of one player does not directly correspond to the game of

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another player. In a non-zero-sum game, it is possible for all the players to win or for all the

players to lose. The classic illustration of a non-zero-sum game is known as the prisoner’s

dilemma. The prisoner’s dilemma hypothesizes that two criminals (prisoner A and prisoner B)

are arrested and charged with the same crime. At the police station, they are separated, and each

is given the following option: if you inform on the other prisoner, you will be set free, while the

other prisoner will receive a five-year sentence. Both prisoners would instinctively recognize

that if they both remained silent, the police would have insufficient evidence to convict both of

the crime. At worst, they would be held in the jail for several months. If, however, both prisoners

informed on each other, they would probably receive a two-year sentence. Assuming that both

prisoners wish to serve the minimal amount of time, their individual decisions will be dictated

by what they believe will be the other prisoner’s decision. There are four possible outcomes to

this scenario:

1. Prisoner A informs on prisoner B while prisoner B remains silent. This is a win for prisoner A and a loss

for prisoner B. This is a win-lose outcome.

2. Prisoner B informs on prisoner A while prisoner A remains silent. This is a win for prisoner B and a loss

for prisoner A. This is a win-lose outcome.

3. Both prisoner A and prisoner B inform on each other. This situation essentially represents a loss for both

prisoner A and prisoner B. This is a lose-lose outcome.

4. Both prisoner A and prisoner B trust each other and remain silent. This results in both prisoners doing a

minimal amount of time. In effect, this is a win-win for both individuals.

The point of this brief introduction to game theory is to highlight the possibility of creating

a win-win scenario. In the prisoner’s dilemma, the key to achieving a win-win outcome is that

both parties must have complete trust in each other. This concept of mutual trust plays a critical

role in successful supply chain management. Far too often, both the supplier and the customer

perceive the relationship as a win-lose outcome only. Customers want suppliers to provide items

at the lowest possible cost, with the highest quality, delivered exactly when needed. Customers

often use multiple suppliers and play them off against each other to guarantee the lowest

possible price. Suppliers want to provide customers with items of the highest possible price,

with acceptable quality, and delivered when it is convenient for the supplier. These attitudes

produce a “dance” between the customer and the supplier, where both are trying to win even if

that means that the other loses. These attitudes often stem from the fact that there is no trust

between the customer and the supplier.

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