What Is The Prisoner’s Dilemma in Game Theory?

Decision-making involves dilemmas where choices that seem rational for an individual can lead to negative results for the group. These strategic interactions are present in economics, politics, and daily life. A famous example of this paradox is the Prisoner’s Dilemma, which comes from game theory. It provides a model for understanding why cooperation is difficult, even when it is mutually beneficial.

Decoding the Prisoner’s Dilemma

The classic Prisoner’s Dilemma scenario, first conceptualized in 1950, involves two suspects arrested for a crime. The police separate them into different rooms with no way to communicate. Lacking the proof for the principal offense, the prosecutor offers each prisoner the same deal to secure a conviction.

Each prisoner faces two choices: cooperate with their partner by remaining silent, or defect by confessing. If both cooperate, they each receive a short sentence, such as one year. If one defects and the other cooperates, the defector goes free while the silent partner receives a harsh three-year sentence. If both defect, they both receive an intermediate sentence of two years.

From an individual’s perspective, confessing is always the better option. If the other prisoner stays silent, confessing leads to freedom instead of a one-year sentence. If the other prisoner confesses, confessing leads to a two-year sentence instead of three. This logic makes confessing the dominant strategy for each person.

Since both prisoners independently conclude that confessing is their best move, they both end up confessing. This outcome is a Nash Equilibrium, a state where neither prisoner can improve their situation by changing their decision alone. The paradox is that by rationally pursuing self-interest, they both receive a two-year sentence, a worse outcome than the one-year sentence they would have received by cooperating.

What is Game Theory?

The Prisoner’s Dilemma is a famous example of game theory, the mathematical study of strategic decision-making. It provides a framework for analyzing situations where the outcome of one person’s choice depends on the choices of others. The field was developed in the mid-20th century by figures like John von Neumann and Oskar Morgenstern.

A “game” has three main components: players (the decision-makers), strategies (the available actions), and payoffs (the outcomes for each combination of strategies). These games can be represented visually using a matrix that shows the payoffs for each player based on their joint decisions, as in the prisoner scenario.

Games are categorized in several ways, including the distinction between zero-sum and non-zero-sum games. The Prisoner’s Dilemma is a non-zero-sum game because cooperation leads to a better mutual outcome than mutual defection. It is also a non-cooperative game, as players make their decisions independently without binding agreements.

Escaping the Dilemma Through Repetition

The outcome of the Prisoner’s Dilemma changes when the game is played repeatedly by the same individuals. This scenario, the Iterated Prisoner’s Dilemma (IPD), introduces reputation and trust. When players know they will interact again, the possibility of future retaliation or reward makes cooperation a more appealing long-term strategy.

In the 1980s, political scientist Robert Axelrod conducted computer tournaments to find the most effective IPD strategy. The winner was a simple strategy called Tit-for-Tat, submitted by psychologist Anatol Rapoport. Tit-for-Tat begins by cooperating on the first move and then mirrors the opponent’s action from the previous round.

Other strategies also exist within the IPD. An “Always Defect” strategy consistently betrays the opponent, which is effective against unconditional cooperators but fails against retaliatory strategies. Another approach is the “Grim Trigger,” where a player cooperates until the opponent defects once, after which the player defects for all subsequent rounds.

Axelrod’s work demonstrated that successful strategies in the IPD shared several properties:

• They were ‘nice’ and never the first to defect.
• They were retaliatory and punished defection.
• They were forgiving and willing to return to cooperation.
• They were clear and easy for the opponent to understand.

The success of Tit-for-Tat showed that strategies built on reciprocity could foster cooperation over time, even in a model based on self-interest.

The Prisoner’s Dilemma in Our World

In economics, the dilemma can model the behavior of two competing companies deciding on advertising budgets. Both firms might be better off if they limit their spending. However, each company has an incentive to increase its advertising to gain market share, leading to a scenario where both spend heavily with little net gain.

International relations provide other examples. During the Cold War, the arms race between the United States and the Soviet Union mirrored the dilemma. While the ideal outcome was to avoid massive military spending, each nation armed itself to avoid a disadvantage, leading to a costly stalemate. A similar dynamic applies to climate agreements, where countries may hesitate to curb emissions for fear of economic disadvantage.

The dilemma also manifests in biology and social situations. Vampire bats, for example, engage in reciprocal altruism by sharing blood meals with roost-mates who have failed to feed. In society, the “tragedy of the commons” describes situations where individuals might over-exploit a shared resource like a fishery. While restraint would preserve the resource, each individual has an incentive to take as much as they can, potentially leading to its collapse.