The Social Contract and The Prisoner's Dilemma

The Prisoner's Dilemma: A Foundational Game Theory Concept

  • Origin: The Prisoner's Dilemma is a core concept from game theory, a branch of social science that merges ideas from economics, politics, and social psychology.

  • Purpose of Game Theory: To analyze strategies in situations where the outcome for each participant depends on the choices of all other participants, aiming to predict rational behavior in strategic interactions.

The Classic Scenario

  • The dilemma typically involves two suspects, arrested for a crime, and held incommunicado in separate cells. The police lack sufficient evidence for a major conviction but have enough for a minor one.

  • Each prisoner is given two options:

    1. Confess (or betray): Implicate the other prisoner.

    2. Remain silent (or cooperate): Not implicate the other prisoner.

The Payoff Matrix (Outcomes and Sentences)

  • The consequences of their choices are structured as follows:

    • If Prisoner A confesses and Prisoner B remains silent: A goes free, B gets 10 years.

    • If Prisoner B confesses and Prisoner A remains silent: B goes free, A gets 10 years.

    • If both confess: Both get 5 years.

    • If both remain silent: Both get 1 year (for the minor charge).

Dominant Strategy

  • A dominant strategy is a strategy that yields the best outcome for a player, regardless of what the other player chooses. In the Prisoner's Dilemma:

    • From Prisoner A's perspective:

      • If B remains silent, A gets 0 years by confessing (better than 1 year by remaining silent).

      • If B confesses, A gets 5 years by confessing (better than 10 years by remaining silent).

    • Therefore, for both prisoners, confessing is the dominant strategy.

Nash Equilibrium

  • A Nash Equilibrium occurs when each player chooses their best strategy, given the choices of the other players, and no player can improve their outcome by unilaterally changing their strategy.

    • In the Prisoner's Dilemma, the Nash Equilibrium is when both prisoners confess (resulting in 5 years each). This is because once one prisoner has decided to confess, the other prisoner cannot improve their own outcome by unilaterally choosing to remain silent.

The Dilemma Explained

  • The paradox lies in the fact that while both prisoners individually act rationally by choosing to confess (their dominant strategy), they both end up worse off (5 years each) than if they had both cooperated and remained silent (1 year each).

  • This outcome illustrates the conflict between individual rationality and collective well-being. The collectively optimal outcome (2 years total) is not stable due to the incentive for individual defection.

Real-World Applications

  • The Prisoner's Dilemma is used to model various real-world situations, including:

    • Oligopolies: Firms deciding whether to cooperate on pricing or engage in price wars.

    • Environmental issues: Nations deciding whether to reduce pollution or free-ride on others' efforts.

    • Arms races: Countries deciding whether to increase military spending.

    • Teamwork: Individuals deciding whether to put in full effort or shirking.