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2018-10-16

The prisoner’s dilemma as a decision-making aid

Games of type of the “prisoner’s dilemma” will play in the business administration have a special role and will be presented so extensively. It is a non-cooperative game with two people, everyone decides for themselves, and simultaneously and can achieve advantages at the expense of the other. But it’s not a pure zero-sum game, i.e., cooperation that could bring both benefits, the interests are strictly opposed. There is interest in harmonies and conflicts at the same time.

In the classic example, from which the game gets its name, is about the length of a prison sentence. Smaller Numbers are for a better result.

Example:

The usual Interpretation of this payoff matrix is the following:

Two of the armed robbery Suspects are arrested and questioned separately. You have no opportunity to deny. Both Suspects have two possible strategies: confess (a1, b1) or confess (a2, b2). In General a1, b1 as the cooperative strategies and a2, b2 as a defektive strategies referred to (to defect = defect, overflow).

The Numbers in the Matrix are to be understood: not to Confess, both of you can condemn it only on account of unlawful possession of a firearm, and you both get two years.

Both confess then they both get 6 years in prison.

Only one confesses then this comes as a key witness unpunished, while the other wanders for 10 years in prison, because he has denied persistent.

It is important that both of them would not be in a cooperation (confess) better than if they betray each other; specifically: to go only two years in prison instead of six years.

But the best is the one, the betrayal of exercises (defektiert), while the other holds tight.

There is a balance point.

Player 1 thinks: If I do not confess (a1) and the other admits (b,2), then country I at 10 years, and my buddy goes home. This is bad. So I confess better. My mate density (b1), then I could by my confession. So I confess better. Confess is the dominant strategy.

Because they both know that each other has a strong incentive to confess, in fact, confess to both of them. Because no one wants to come in, the Situation of the “Exploited” that holds self-sealing, and then alone for up to 10 years in prison. In the case of a2, b2 is a Nash equilibrium.

The Dilemma lies in the fact that both land by selecting their respective best strategy is inevitable in the case of a Situation, which is clearly worse than any other. The balance point is not at the same time, the best solution for the players.

This basic figure can be transferred to many situations:

Examples

For two companies in the Dyopol it would be better if you keep both of your prices. Even better would be for the individual, his company could unilaterally reduce the price and thus the market, to deduct shares from the competitors. Since both

fear to lose market shares, lower both the prices and make less profit to win market shares.

With the threat of Overfishing the world’s oceans, it would be better for all Concerned to use the proper nets with a wide mesh so that the fish offspring in the sea. For each fisherman, but it is even more lucrative if the other stick to the rules, and he even fished with small-meshed nets, and picks up a particularly large catch. Since the other need, the fear, the fish finally all with fine-meshed nets and damage, ultimately, self-solid, by the life-destroying basis.

Two parties competing for the voters ‘ favor, do not dare to austerity measures announced the budget deficit. For each party it would be better, the other would propagate painful cuts, while paying themselves generously. Because then you can expect the most votes. So it comes to a Situation that is not saved, even though both parties know that that would be actually necessary and useful.

 

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Image source: (c) Lupo / pixelio.de

The Text comes from the teaching and textbook of Professor Göbel: decisions in companies.

 

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