Prisoner's dilemma

Definition

The prisoner's dilemma is a fundamental concept in game theory that illustrates how two rational individuals may not cooperate, even if it appears that it is in their best interest to do so. This scenario shows that when both players choose to betray each other, they end up worse off than if they had cooperated, highlighting the conflict between individual self-interest and mutual benefit. It connects to strategies where players can either choose pure strategies—consistently making one choice—or mixed strategies, where they randomize their decisions based on probabilities, as well as the identification of dominant strategies that could lead to suboptimal outcomes.

5 Must Know Facts For Your Next Test

1. In the classic prisoner's dilemma, two criminals are arrested and interrogated separately; each has the option to either betray (defect) or remain silent (cooperate).
2. The outcome where both players betray each other results in a worse payoff for both compared to if they had cooperated by remaining silent.
3. Even though mutual cooperation yields a higher collective payoff, individual rationality leads both players to defect, which is known as a dominant strategy in this scenario.
4. The prisoner's dilemma demonstrates how collective action problems arise in economics, environmental issues, and politics when individuals prioritize self-interest over group benefit.
5. Repeated iterations of the prisoner's dilemma can lead to different strategies, such as tit-for-tat, where players begin cooperating and then mimic their opponent's previous move.

Review Questions

• How does the prisoner's dilemma illustrate the conflict between individual rationality and collective benefit?
  • The prisoner's dilemma shows that while each individual player acting rationally chooses to betray the other for immediate self-gain, this decision leads to a collectively worse outcome. If both players choose to remain silent, they achieve a better result together than if they betray each other. This highlights the struggle individuals face when balancing self-interest with the potential benefits of collaboration, which can result in mutual advantage if both parties choose cooperation.
• Discuss how the concept of dominant strategies applies within the framework of the prisoner's dilemma.
  • In the prisoner's dilemma, each player faces a dominant strategy: to defect. This means that regardless of what the other player chooses, betraying them always provides a better payoff than cooperating. Consequently, this leads to both players choosing to defect, even though mutual cooperation would yield higher payoffs. The presence of these dominant strategies is crucial for understanding why rational individuals may fail to cooperate despite clear benefits.
• Evaluate how mixed strategies might change the outcomes in a repeated prisoner's dilemma scenario.
  • In a repeated prisoner's dilemma, players have the opportunity to adopt mixed strategies instead of sticking to pure defection or cooperation. By randomizing their choices based on past interactions or perceived likelihood of cooperation from others, players can create an environment conducive to trust and collaboration over time. Strategies like tit-for-tat can emerge, allowing players to start with cooperation and respond based on previous actions. This dynamic illustrates how long-term interactions can shift equilibria from purely self-interested outcomes towards cooperative ones.

Related terms

Nash Equilibrium: A situation in a strategic game where no player can benefit by changing their strategy while the other players keep theirs unchanged.

Payoff Matrix: A table that describes the payoffs for each player based on the combination of strategies chosen by all players in a game.

Cooperative Game: A type of game where players can negotiate binding contracts and work together to achieve a better outcome than what they could achieve individually.