The year is 1962, and the United States has discovered that the Soviet Union has built secret missile bases in Cuba. Tensions are high, with both sides poised to launch nuclear attacks if provoked.
World leaders must decide whether to cooperate through diplomacy or defect by engaging in an arms race. In today’s world, leaders across every sector—business, economics, politics—have to acknowledge the human condition of not wanting to work together.
All leaders have to navigate the prisoner’s dilemma.
Maybe you’re familiar with it. It’s a decision faced by two captured prisoners, each presented with the option to betray the other or remain silent. This scenario is known as the prisoner’s dilemma game. Since its origins in 1950, nearly 50,000 scholarly articles have analyzed the implications of the prisoner’s dilemma in fields ranging from political science to evolutionary biology.
At its core, the prisoner’s dilemma involves decisions driven by self-preservation. It provides insight into why cooperation is often challenging to achieve, even when it provides the best outcome for the group.
By examining the incentives and payoffs that drive decision-making, we can better understand group dynamics in situations from corporate negotiations to international relations.
- The prisoner’s dilemma paradigm elegantly illustrates the challenges of achieving cooperation between self-interested agents, even when it leads to the best overall outcome.
- Developed in 1950 as an abstract thought experiment to model decision theory, the prisoner’s dilemma is the most analyzed scenario in gamer theory. It’s still being analyzed, refined, and put under academic scrutiny today.
- Its applications range from philosophy, biology, politics, economics, and even artificial intelligence.
- Because so many problems require teamwork and collective decision-making, it is imperative for leaders to understand the complexity of human cooperation.
What is the Prisoner’s Dilemma?
The prisoner’s dilemma is a game theory thought experiment that involves two rational decision-makers (or “agents”), each of whom has the option to cooperate for mutual benefit or betray their partner (“defect”) for individual reward.
Two prisoners are interrogated separately and given the choice to either confess to their crimes or remain silent. If one confesses while the other remains silent, the confessor goes free while the silent accomplice receives a long sentence. If both confess, they each receive a reduced sentence. If both remain silent, they each receive a short sentence due to lack of evidence. The payoff matrix incentivizes confession over cooperation even though remaining silent provides the best total outcome.
The prisoner’s dilemma game elegantly demonstrates concepts like dominant strategy and Nash equilibrium, providing insights into group dynamics involving cooperation and self-interest. It is likely the most analyzed scenario in game theory.
Background on the Prisoner’s Dilemma
The prisoner’s dilemma originated as a mathematical model designed by Merrill Flood and Melvin Dresher in 1950 while working at the RAND Corporation. It was formalized and named the “prisoner’s dilemma” by Princeton mathematician Albert Tucker.
Specifically, they were interested in modeling the dynamics between two rational participants and how they would choose between cooperating for mutual benefit or betraying the other for individual gain.
While first conceived as a mathematical abstraction, Princeton mathematician Albert Tucker soon after formalized the scenario by framing it as a story involving two prisoners. This gave the concept a more concrete framing that helped demonstrate the counterintuitive outcomes.
The prisoner’s dilemma game quickly became influential in the emerging field of game theory in the 1950s. Early game theorists like John Nash recognized how the model could provide insight into real-world economic, political, and social interactions. It revolutionized the analysis of cooperation, competition, and group dynamics across disciplines ranging from economics to evolutionary biology.
The classic story goes that two criminals are arrested for a crime they committed together. The police lack sufficient evidence to convict them for the principal charge, so they separate the prisoners and offer each the same deal: If one confesses and their partner does not, the confessor will be released immediately while the partner will spend 20 years in prison. If both confess, they will each get 5 years. If both remain silent, they will be tried for lesser crimes with 1 year in prison.
- Prisoner B remains silent:
- Prisoner A remains silent: Each serves 1 year
- Prisoner A confesses: A goes free, B serves 20 years
- Prisoner B confesses:
- Prisoner A remains silent: A serves 20 years, B goes free
- Prisoner A confesses: Each serves 5 years
The payoff matrix illustrates that confession is the dominant strategy—it is better to confess regardless of the partner’s choice. Yet, both prisoners remaining silent produces the best total outcome. This demonstrates the challenge of cooperation—it depends on trusting the other party without knowing their decision.
The equilibrium where both prisoners confess represents a Nash equilibrium, where neither has the incentive to change their strategy on their own.
The prisoner’s dilemma paradigm revolutionized the analysis of group dynamics. Game theorists like John Nash realized that most real-world interactions between rational participants could be modeled as non-zero-sum games involving cooperation and betrayal, with payoff matrices analogous to the prisoner’s dilemma. This enabled new insights into economics, international relations, and evolution.
The prisoner’s dilemma game exemplifies key concepts in game theory, including dominant strategy, Nash equilibrium, Pareto efficiency, and Pareto inferiority. Understanding the incentives of the payoff matrix provides insights into achieving mutually beneficial cooperation in multi-agent scenarios.
Examples of the Prisoner’s Dilemma
While initially an abstract thought experiment, the prisoner’s dilemma game has been recognized as a valuable model for many real-world group dynamics situations. Here are some examples that mirror the incentives and payoffs of the classic formulation:
- Nuclear Armament: The military buildup between the United States and the Soviet Union during the Cold War is a frequently cited example. If both sides refrain from acquiring more nuclear weapons (cooperate), the result is peace. If one nation builds more bombs while the other practices restraint (defects), they gain a military advantage. If both engage in an arms race (mutual defection), the end result is a dangerous world, but with the balance of power maintained. Refraining from an arms race provides the best total outcome, but the incentives push toward defection.
- Oligopolistic Price Fixing: Consider two large companies that dominate a market. If they cooperate by fixing high prices, they both earn large profits. If one company lowers prices to undercut the competitor while the competitor maintains high pricing (defection vs. cooperation), the defector gains market share. If both lower prices to compete (mutual defection), neither dominates, but they earn lower profits due to competition. Maintaining high prices is the best outcome of cooperation, but the incentives favor defection.
- Friendship: Imagine two friends on a test. If they both cheat by sharing answers (defect), they pass but may get caught. If one remains honest while the other cheats (cooperation vs. defection), the cheater succeeds while the honest one fails. If both are honest (cooperate), they have a high chance of passing and avoiding punishment. Honesty provides the best total outcome, but with uncertainty about the other’s choice, the incentives push toward defection.
These everyday examples mirror the payoff matrix and demonstrate why cooperation, while beneficial to the group, is difficult to achieve due to fear of betrayal and pursuit of self-interest. The prisoner’s dilemma manifests itself in interactions ranging from personal relationships to nuclear brinkmanship.
Applications of the Prisoner’s Dilemma
“The two-person iterated Prisoner’s Dilemma is the E. coli of the social sciences, allowing a very large variety of studies to be undertaken in a common framework.”—Robert Axelrod, The Complexity of Cooperation
The prisoner’s dilemma has been recognized as a foundational model that provides insights across many fields. Here are some relevant real-world applications:
- Economics: In economics, the prisoner’s dilemma helps illustrate how rational self-interest can lead to inferior outcomes in markets. For instance, it explains why oligopolies can result in higher consumer prices (lack of competition from price fixing) or price wars (competition pushing prices below optimal levels). Economics research utilizes game theory models built on the prisoner’s dilemma framework to analyze topics ranging from trade negotiations to competition policy.
- Evolutionary Biology: In evolution, the prisoner’s dilemma provides insights into how cooperation and “tit for tat” retaliation develop between competing species. Biologists construct payoff matrices for scenarios like predator-prey relationships and the symbiotic behaviors of different organisms to examine how cooperative behaviors are naturally selected over time. Work by researchers like the late evolutionary biologist Robert Trivers used the prisoner’s dilemma model to understand altruism and cooperation better.
- Political Science: In political science, the prisoner’s dilemma gives insight into conflict avoidance models like mutually assured destruction. For instance, it framed analysis of nuclear armament during the Cold War, as unilateral buildup incentivized the other nations to follow suit, resulting in a dangerous arms race. Defection from non-proliferation treaties threatens to put nations in prisoner’s dilemma scenarios with suboptimal outcomes. The model provides perspective into balancing cooperation and self-preservation in international relations.
The wide relevance of the prisoner’s dilemma illustrates the power of its game theory approach to cooperation versus competition.
The Value of Understanding the Prisoner’s Dilemma
“Strange game. The only winning move is not to play.”—WarGames
The concept of the prisoner’s dilemma sheds light on why it’s difficult to achieve cooperation for the greater good when individuals prioritize their own self-interest. By understanding the motivations that might lead rational actors to choose betrayal over collaboration, we can find ways to overcome obstacles to cooperation.
Some key lessons provided by the prisoner’s dilemma include:
- The need for communication and transparency in order to align incentives
- Establishing reciprocity and trust between participants
- Understanding how the long-term benefits of cooperation can override short-term selfish interests
- Recognizing how group morale improves overall outcomes
- Applying strategies like tit-for-tat punishment of defection and forgiveness after retribution
The prisoner’s dilemma game applies to various real-world scenarios beyond the original version. Knowing how the payoff matrix influences decision-making can enhance group cooperation, such as in business ventures, economic policy, or international relations.
Even after 70 years, this model still provides valuable insights into achieving mutually beneficial outcomes in group dynamics involving cooperation and competition.
Learn more about the complex nature of human cooperation with a study on Machiavellianism.
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- Stanford Encyclopedia of Philosophy. (2007, August 29). Prisoner’s dilemma. https://plato.stanford.edu/entries/prisoner-dilemma
- Shoukry, A., González-Díaz, G., & Nedić, A. (2021). A prisoner’s dilemma game with imperfect observation. PLOS ONE, 16(12), e0260615. https://doi.org/10.1371/journal.pone.0260615
- Roberts, E. S. (1999). Applications of game theory: The prisoner’s dilemma. CSLI, Stanford University. https://cs.stanford.edu/people/eroberts/courses/soco/projects/1998-99/game-theory/applications.html
- Policonomics. (n.d.). The prisoner’s dilemma game theory. https://policonomics.com/lp-game-theory2-prisoners-dilemma/
- WGBH American Experience. (n.d.). John Nash and the prisoner’s dilemma. https://www.pbs.org/wgbh/americanexperience/features/nash-game/
- Cornell University INFO 2040. (2015, September 11). United States vs. Soviet Union: The prisoners’ dilemma. https://blogs.cornell.edu/info2040/2015/09/11/united-states-vs-soviet-union-prisoners-dilemma/
- Axelrod, R. (2006). The complexity of cooperation: Agent-based models of competition and collaboration. Princeton University Press. https://press.princeton.edu/books/paperback/9780691015675/the-complexity-of-cooperation
- Rand, D. G., & Nowak, M. A. (2013). Human cooperation. PNAS, 110(25), 10404-10405. https://doi.org/10.1073/pnas.1306480110
- My Geek Wisdom. (2016, May 21). A strange game. The only winning move is not to play. https://mygeekwisdom.com/2016/05/21/a-strange-game-the-only-winning-move-is-not-to-play/