Overview and Definition
The prisoner’s dilemma is a popular example used in game theory that demonstrates why two completely rational individuals might not cooperate, even when it is in their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher in 1950 while working at RAND. The name “prisoner’s dilemma” and the version with prison sentences as payoffs was developed by Albert Tucker when he wanted to make Flood and Dresher’s ideas more accessible to an audience at Stanford University in the same year.
The prisoner’s dilemma shows why two rational individuals might not cooperate even when it is in their best interests to do so. It is a type of non-zero-sum game in which the optimal outcome is not obtained by both players acting in their own rational self-interests. The premise of the thought experiment is that two suspects, A and B, are arrested and interrogated separately for a major crime. Prosecutors have enough evidence to convict both suspects on a lesser charge, but not enough to convict them on the more serious charge unless at least one of them confesses and testifies against the other. The prisoners are offered deals and given the choice to either cooperate with each other or betray each other.
The prisoner’s dilemma can be summarized with the following payoff matrix:
| Prisoner B stays silent | Prisoner B betrays | |
|---|---|---|
| Prisoner A stays silent | Each serves 1 year | Prisoner A: 3 years Prisoner B: goes free |
| Prisoner A betrays | Prisoner A: goes free Prisoner B: 3 years | Each serves 2 years |
Each prisoner has two options: to either cooperate with their accomplice and stay silent, or to betray them and testify against them. The outcomes and consequences differ depending on what both prisoners choose to do.
- If A and B both stay silent (cooperate), each of them will only serve 1 year in prison on the lesser charge.
- If A betrays B but B remains silent, A will go free while B will serve 3 years in prison.
- If B betrays A but A remains silent, the opposite happens.
- If A and B both betray each other, both of them will serve 2 years in prison.
The paradox and dilemma is that if the prisoners were able to cooperate, they would minimize their total prison time by both staying silent. But from an individual prisoner’s perspective, they are better off betraying their accomplice in order to avoid the worst-case scenario of 3 years in prison. The rational choice for each prisoner is to betray the other, even though this results in a longer total prison time. This demonstrates the conflict between collective and individual rationality.
History and Origins
The prisoner’s dilemma exemplifies the tension between individual and group rationality that was first formally studied in game theory. The thought experiment itself was originally framed by Merrill Flood and Melvin Dresher in 1950 while working at RAND. It was later formalized and named “prisoner’s dilemma” by Albert Tucker at Stanford.
Work of Flood and Dresher at RAND
Merrill Flood and Melvin Dresher created the model while working at RAND in 1950. RAND was a think tank where scholars were focused on research and analysis related to armed forces and national security.
Flood and Dresher’s original model involved two suspects being interrogated for a major crime. The prosecutors tell each prisoner that they can either confess and testify against the other suspect, or keep quiet. The suspects are held separately and cannot communicate or coordinate with each other. Based on both of their choices, each will receive a different prison sentence.
This presented a scenario where pursuing individual gain can lead to a worse result than if the prisoners had cooperated with each other and remained silent. Even though their model revealed the benefits of cooperation, it showed how rational individuals might not cooperate.
Albert Tucker Formalizes “Prisoner’s Dilemma”
Later in 1950, Albert Tucker formalized Flood and Dresher’s model and gave it the “prisoner’s dilemma” name. Tucker was a mathematician at Stanford University who wanted to make their ideas more accessible to a wider audience.
Tucker presented the prisoner’s dilemma as a game theory matrix with prison sentences as payoffs. This popularized the idea and made it easier to understand. The name “prisoner’s dilemma” and the version with prison sentence payoffs stuck and became well known.
The prisoner’s dilemma became one of the most widely used models in game theory and social science. It demonstrated how groups fail to cooperate even when it is in their mutual best interest to do so. This revealed important ideas about human psychology and the tension between individual and collective rationality.
Real World Examples
The prisoner’s dilemma concept can be applied to many real world situations involving conflicts of interest between groups and individuals. Some common examples include:
- Oligopolies: A small number of large companies dominating a market. It is in their shared interest to avoid aggressive price wars, but each company individually has incentive to undercut the others to gain more market share.
- The Tragedy of the Commons: Individuals sharing a common resource have incentive to overuse it for personal gain, which depletes the resource contrary to the group’s long-term interests. Examples include overfishing, overgrazing, and air pollution.
- Advertising Races: Advertising spends end up higher than ideal for companies when each one tries to out-do the others. If they cooperatively agreed to advertise less, they could cut expenses while still informing consumers.
- Price Wars: When one company lowers prices, competitors feel compelled to lower prices also. They may be better off avoiding these “races to the bottom.”
- Nuclear Deterrence: The concept of mutually assured destruction relies on enemy nations not launching nuclear first strikes for individual gain since the ensuing retaliation would ensure mutual destruction.
- Labor Negotiations: During strikes, management and labor unions often resist agreement, hurting both, rather than compromising to reach a deal.
- Social Dilemmas: Issues like climate change and vaccination require individual sacrifice for the collective good.
The prisoner’s dilemma model effectively demonstrates how rational decisions by individuals can lead to sub-optimal outcomes for the overall group in many situations. It provides insights into human psychology and behavior.
Strategies and How to “Win”
Over the years, there have been various strategies developed for how to “win” iterations of the prisoner’s dilemma. These strategies aim to produce the optimal outcome where both parties receive the minimum, lightest sentences.
Cooperating Initially
One strategy is to first signal to the other player that you will cooperate by staying silent on the first move. If both prisoners understand it is in their mutual interest to stay silent, cooperating on the first move can signal that they should continue cooperating going forward.
Tit for Tat
With repeated plays of the prisoner’s dilemma, the “tit for tat” strategy gained popularity. It starts with cooperation, and then mirrors whatever the other player chose on the prior move. Tit for tat signals cooperation initially but retaliates against betrayal. Studies showed it produced good outcomes.
Forgiving Tit for Tat
The “forgiving tit for tat” variant cooperates even after the other player defects. Occasional forgiveness helps recover from getting stuck in betraying patterns.
Random or Mixed Strategies
Strategies that randomly pick between cooperating and defecting on each turn can reduce how exploitable the strategy is. The randomness makes the strategy harder to take advantage of.
Learning Models
Machine learning models can develop their own strategies by repeatedly playing against various opponents and learning what works best. These learned strategies often involve elements of randomness, cooperation, and retaliation. The models learn that some forgiveness helps produce better long-term outcomes.
There is no one definitive strategy for solving prisoner dilemma games. Context, the behavior of the other player, and whether the game is played once or repeatedly all influence optimal strategies. But signaling initial cooperation, retaliating to promote cooperation, and occasional forgiveness tend to produce good results. The key is to establish mutually cooperative outcomes.
Key Takeaways and Lessons Learned
The prisoner’s dilemma game model reveals some important insights about human psychology and cooperation:
- Individuals acting in self-interest does not always produce optimal group outcomes.
- There are conflicts and tensions between rational decisions by individuals versus groups.
- Complete rationality does not necessarily lead to cooperation and coordinated outcomes.
- Signaling cooperativeness, retaliating against uncooperative behavior, and occasional forgiveness are strategies that can promote mutually optimal solutions.
- Repeated interactions over time enable learning, reciprocity, and cooperation to develop.
- Some central authority or coordination may be needed to enforce cooperation as the optimal solution in certain contexts.
The model is simplistic but shows how independent and rational decision-making can lead to less than ideal results for both parties. These insights contributed significantly to the field of game theory and our understanding of human psychology. The dynamics modeled by the prisoner’s dilemma permeate many aspects of economics, politics, and everyday social interactions.
Questions and Answers
Here are some common questions about the prisoner’s dilemma:
What is the main point of the prisoner’s dilemma?
The main point is to show how two completely rational individuals may not cooperate even when it is in their mutual best interests to do so. It reveals the conflict between rationality at the individual level versus the group level.
Why is it called a “dilemma”?
It’s a dilemma because the prisoners are faced with a difficult choice where opting for individual gain conflicts with the better group outcome of mutual cooperation. There is no clear rational path that satisfies both the individual and group interests.
Is the prisoner’s dilemma a one-time or repeated game?
The prisoner’s dilemma can be analyzed both as a one-time, simultaneous-move game and as a sequential-move game that is repeated multiple times. Different strategies emerge depending on whether the game is played once or repeatedly.
What is a “Nash Equilibrium”?
A Nash Equilibrium is a stable scenario where each player holds the optimal strategy given the other players’ choices. In the prisoner’s dilemma, mutual betrayal is the Nash Equilibrium even though mutual cooperation would be better for both.
How does the prisoner’s dilemma relate to real world examples?
The individual vs. group interests dynamic shown in the prisoner’s dilemma model can be applied to many real world situations including economics, nuclear deterrence, climate change, strikes, and social dilemmas.
What are some key strategies for solving the dilemma?
Strategies like cooperating initially, tit-for-tat, occasional forgiveness, and mixed play help promote mutually beneficial outcomes in repeated prisoner dilemma games. Signaling cooperativeness while retaliating against uncooperative moves tends to work well.
Conclusion
In conclusion, the prisoner’s dilemma is a landmark concept in game theory and social science. The model elegantly demonstrates how rational decision-making by individuals can lead to sub-optimal outcomes for the group. It reveals tensions between individual and collective rationality. The prisoner’s dilemma framework can be applied to economics, politics, psychology, and many real world situations. Strategies of signaling cooperativeness, retaliating, and occasional forgiveness help produce good outcomes. The model provides profound insights into human nature and cooperation that contributed greatly to the fields of mathematics, economics, psychology, politics, and philosophy. Overall, the prisoner’s dilemma is a thought-provoking example of individual interests conflicting with the greater good.