# Potential solutions of the $n$-player Prisoner's Dilemma

Suppose we want to model a real-world phenomenon as an $$n$$-player Prisoner's Dilemma.

To be more specific, suppose we use RM Dawes' paper "The commons dilemma game: An n-person mixed-motive game with a dominating strategy for defection, 1973" which generally formalize the Prisoner's Dilemma for $$n$$ players along with a tragedy of the commons (Hardin's tragedy 1968).

Although modelling might seem "easy," how one can properly analyze in Game theory? How can we justify the validity of the game with the real world?

Also, even if we model the real-world phenomenon as a Prisoner's Dilemma, what would be some of the potential solutions to prevent the tragedy?

To be more exact, what are some of the standard methodologies to prevent universal defection?

I'd appreciate any help.

All the insights to your question about the n-player game carry over from the 2-player game.

The validity in the real world is justified to the extent and in the same way as for the 2-player game, with all its caveats. An n-player game, however is even more realistic, because it is more general and many economic issues involve more than 2 players. Consider for example global geopolitical issues that require coordination, such as climate change or nuclear bombs.

The potential solutions are the same as for the 2-player game as well. Notably, in repeated games over time, reputational effects and retaliation can matter. If those who play the non-cooperative strategy (which is the "bad" action that leads to the prisoner's dilemma outcome that is worse for everyone) are punished over time, then the problem you describe can be overcome. Denesp in his comment to this answer gives some examples.

The reason a static prisoner's dilemma always has a non-pareto-optimal equilibrium (i.e. why it poses a societal problem) is because it is played once or is a one-shot game without the possibility to punish deviators later on. If players interact frequently with each other, (the threat of) retaliation can help overcome the dilemma. There are a number of such strategies. One of the more famous ones to look up would be "tit for tat".

• I would hesitate to say that "a static prisoner's dilemma has no solution". It has an equilibrium. If you mean there is no Pareto-optimal equilibrium, that is true. If you mean there is no way to make a Pareto-optimal outcome an equilibrium, that depends on what we consider a "way". In many real world situations modeled like this the policy planner could implement punishments or transfers to change the payoffs of the make. E.g. most people do not like to pay taxes, even though we use the infrastructure. But they do, not out of a sense of civic duty, but because avoidance was made costly. – Giskard Feb 23 '19 at 8:41
• I meant solution in the terms OP meant it, as in a pareto optimal outcome (or pareto improvement to the dominant strategy). That's a good point and I will edit the answer to clarify. However I don't see how the "ways" you consider apply to a static one-shot game and I do discuss your suggestions in the context of repeated games. – BB King Feb 23 '19 at 12:25
• An example: In a Prisoner's dilemma the maffia might say that whoever cooperates with the police will be punished. This is not punishment in the sense of a repeated game, but punishment in the sense that the payoffs of the one-shot game are altered. This is a policy type solution to a problem that may be modeled by the prisoner's dilemma. – Giskard Feb 23 '19 at 13:33
• @denesp when you say "punishment" in the case of cooperation, do you mean that the payoffs are affected negatively? – johnny09 Feb 23 '19 at 23:15
• Yes, I use the word in the everyday sense. – Giskard Feb 24 '19 at 7:18