The Prisoner’s Dilemma is typically considered a game of complete information. In this classic game theory scenario, both players are fully aware of the structure of the game, the strategies available to them, and the payoffs associated with each combination of strategies. Here’s why:

Characteristics of the Prisoner’s Dilemma

  1. Complete Information:
    • Payoff Knowledge: Each prisoner knows the consequences (payoffs) of both confessing and remaining silent, given the possible actions of the other prisoner.
    • Common Knowledge: The structure of the game and the payoffs are common knowledge. Both prisoners know that the other prisoner is aware of these payoffs.

Example and Explanation

Payoff Matrix:

  Prisoner B: Silent Prisoner B: Confess
Prisoner A: Silent Both get 1 year A gets 3 years, B goes free
Prisoner A: Confess A goes free, B gets 3 years Both get 2 years
  • If both remain silent: Each serves 1 year.
  • If both confess: Each serves 2 years.
  • If one confesses and the other remains silent: The confessor goes free, and the silent prisoner serves 3 years.

Analysis

  • Complete Information: Each prisoner knows the payoffs associated with each action and knows that the other prisoner also knows this.
  • Not Asymmetric Information: There is no asymmetry in the information; both players have the same information about the game’s payoffs.
  • Not Incomplete Information: There is no uncertainty about the payoffs or the strategies available to the players.

Payoff Matrix

  Player 2: Cooperate Player 2: Defect
Player 1: Cooperate (-1, -1) (-3, 0)
Player 1: Defect (0, -3) (-2, -2)

 

both players have a dominant strategy: “defect”

In the classic Prisoner’s Dilemma, there is exactly one Nash equilibrium which not optimal.

If both players choose MINIMAX strategy they will reach optimal solution and both will defect.

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