Understanding Prisoner's Dilemma: Bi-Matrix, Relationships, and Strategies
What are the key components of a prisoner's dilemma game?
In a prisoner's dilemma game, what is the relationship between the payoffs a, b, c, and d? How do the sets S1 and S2 come into play? And what are the values of u1(Confess, Quiet) and u2(Quiet, Quiet)?
Exploring the Components of a Prisoner's Dilemma Game
When analyzing a prisoner's dilemma game, it is essential to understand the bi-matrix that represents the possible outcomes for each player based on their decisions:
Bi-Matrix:Player 2 Confess Quiet Player 1 Confess (a, a) (c, d) Quiet (d, c) (b, b)
The relationship between a, b, c, and d is crucial in determining the payoffs for each player. Typically, the relationship follows the pattern a > c > d > b, indicating that the payoff for both players confessing is highest, followed by one player confessing and one remaining quiet, with the lowest payoff for both players staying quiet.
The sets S1 and S2 represent the strategies available to each player:
Strategies:S1 = {Confess, Quiet} - Available strategies for Player 1.
S2 = {Confess, Quiet} - Available strategies for Player 2.
The values of u1(Confess, Quiet) and u2(Quiet, Quiet) indicate the payoffs for each player based on their chosen strategies. The specific values would vary depending on the assigned payoffs for each outcome in the game.