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What is a Multi-Person Prisoner’s Dilemma?

We describe the problem of cleaning a student kitchen and use it to illustrate some characteristics of a Multi-Person Prisoner’s Dilemma.
People walking on a city street
© ACTISS

In this article we will list the main characteristics of a Multi-Person Prisoner’s Dilemma and illustrate them with the student kitchen example.

A Multi-Person Prisoner’s Dilemma is a game that has the following characteristics:

  • n persons with the same payoff structure;
  • 2 actions to choose from, one of them is always preferred;
  • whatever you do, you benefit from the others choosing their non-preferred action;
  • there is such a number k that if k people gather and choose their non-preferred alternative together, they get higher payoffs than if they chose their preferred alternatives.

In case of our kitchen story there are 3 persons with the same payoff structure who can either clean or not clean. No matter what the others do, it’s always better not to clean and on the other hand – everyone benefits from the others choosing to clean.

As for the last part of the definition – we have to think about how many people are better off when they decide to clean together instead of staying in a dirty kitchen? In this case it takes only 2 persons to achieve this goal. If Anna and Ben decide to clean they get 1 point each, which is better than 0. It’s important that it doesn’t solve the problem by itself. Both of them are still tempted not to clean.

The Multi-Person Prisoner’s Dilemma relates to a wide array of situations where people are tempted to avoid costs or not to contribute to something that they share with others. And if everyone follows this temptation, everyone is worse off than they would be if they had managed to cooperate (a non-optimal solution). We’ll see some examples of such situations in the next steps.

© ACTISS
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Understanding Human Behaviour: Introduction to Game Theory and Shared Resources

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