8.3.4.2.2. 3P Prisoners’ Dilemma

General Information

The Prisoner’s Dilemma can be extended to involve three players, creating what is known as a 3-player Prisoner’s Dilemma game. In this scenario, three individuals face a situation where they must decide whether to cooperate or betray each other, with the outcomes determined by the combined choices made by all three players. The setup involves a payoff matrix that outlines the possible outcomes and associated payoffs for each player based on their choices.

Each player has two possible choices: “Confess” or “Not Confess”. The outcomes are determined based on the combination of choices made by all three players. The challenge is that, similarly to the 2-player version, there is a conflict between individual rationality and collective optimality.

The players individually have an incentive to not confess, as not confessing typically yields a higher payoff for the individual, regardless of the choices made by others. However, if all players not confessing, the collective outcome may be suboptimal compared to a scenario where all players cooperate.

Analyzing and solving a 3-player Prisoner’s Dilemma involves considering the strategic interactions among all three players, understanding the incentives for cooperation and betrayal, and exploring whether there are any stable strategies or equilibria in the game. The extension to more players adds complexity to the decision-making dynamics and strategic considerations.

This game can be imported, as follows:

from mlpro.gt.pool.native.games.prisonersdilemma_3p import PrisonersDilemma3PGame

Player, Coalition, and Competition

In the context of the Prisoner’s Dilemma, there are threee players, often referred to as Player 1, Player 2, and Player 3. The situation involves three individuals who have been accused of committing a crime together and are now being held in separate cells, unable to communicate with each other. The choices available to each player are either to “Confess” or “Not Confess”. The outcomes and associated payoffs for each player depend on the combination of choices made by all individuals.

Payoff Matrix

(P1, P2, P3)

P2: Confess, P3: Confess

P2: Confess, P3: Not Confess

P2: Not Confess, P3: Confess

P2: Not Confess, P3: Not Confess

P1: Confess

(2, 2, 2)

(5, 5, 1)

(5, 1, 5)

(10, 1, 1)

P1: Not Confess

(1, 5, 5)

(1, 10, 1)

(1, 1, 10)

(15, 15, 15)

Solvers

Player

Solvers

1

Random Solver, Min Greedy Solver

2

Min Greedy Solver

3

Random Solver, Min Greedy Solver

Cross References

Citation

If you apply this game in your research or work, do not forget to cite us.