Free Printable Worksheets for learning The Prisoner's Dilemma at the College level

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Word	Definition
dilemma	a situation in which a difficult choice has to be made between two or more alternatives, especially equally undesirable ones.
prisoner	a person held in prison, especially one serving a sentence of more than a year.
dilemma	a situation in which a difficult choice has to be made between two or more alternatives, especially equally undesirable ones.
payoff	a benefit received.
betray	to be disloyal to someone and tell their secrets, or to break a promise or an agreement
cooperate	to work together with someone else to achieve something that you both want
strategy	a plan of action for achieving a specific goal.
game	a competitive activity or sport in which players contend with each other according to a fixed set of rules.
incentive	something that motivates a person to take action, especially one that is offered as a reward or encouragement.
optimal	best or most favorable.
rational	based on clear thought and reason.
mutual	experienced or done by two or more people, groups, or organizations together, or affecting them all.
defect	to fail to fulfill an obligation or to withdraw support or help from someone, often in a time of need.
equilibrium	a state of balance or stability achieved through the interaction of opposing forces.
dominant	most important, powerful, or influential.
payoff matrix	a table that shows the payoffs that each player in a game receives for every possible combination of actions by the players.
iteration	the repetition of a process or utterance.
Nash Equilibrium	a situation in which each player in a game chooses a strategy that is optimal given the strategies chosen by the other players, resulting in no player having an incentive to change their strategy.
non-zero sum	a type of game in which the gains and losses of the players do not sum to zero, meaning that when one player benefits, others are not necessarily worse off.
strategy	a plan of action for achieving a specific goal.

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Study Guide: The Prisoner's Dilemma

Introduction

The Prisoner's Dilemma is a classic game theory problem that is frequently used to study human behavior in various fields, including economics, political science, and psychology. This study guide will explore the basics of the Prisoner's Dilemma and provide an overview of key concepts.

Basics of the Prisoner's Dilemma

The Prisoner's Dilemma is a game where two players must make a decision without knowing what the other player will do. Each player has two choices: cooperate or defect. The outcomes of the game depend on the choices of both players. The following matrix shows the payoffs for each player:

	Player 2 Cooperates	Player 2 Defects
Player 1
Cooperate	(3, 3)	(0, 5)
Defect	(5, 0)	(1, 1)

As seen in the matrix, if both players cooperate, they both receive a reward of 3. If one player cooperates and the other defects, the defector receives a higher reward while the cooperator receives a lower reward. If both players defect, they both receive a small reward of 1.

Rationality and Dominant Strategy

In game theory, players are assumed to be rational actors who will make decisions that maximize their own payoff. A dominant strategy is a strategy that will always yield the highest possible payout for a player, regardless of the other player's strategy. In the Prisoner's Dilemma, there is a dominant strategy for each player to defect, since no matter what the other player does, the player who defects will receive a higher payoff.

Nash Equilibrium

A Nash Equilibrium is a situation in a game where neither player has an incentive to change their strategy, given the other player's strategy. In the Prisoner's Dilemma, the Nash Equilibrium is for both players to defect, since neither player can gain a higher payoff by switching to cooperate.

Iterated Prisoner's Dilemma

The Iterated Prisoner's Dilemma is a variant of the game where each player plays multiple rounds of the game with the same opponent. In this version, players can use their opponent's previous moves to inform their current decision.

Conclusion

The Prisoner's Dilemma is a fundamental concept in game theory that has important implications for understanding human behavior. It demonstrates the challenges of cooperation in situations where the best outcome depends on mutual cooperation, but there are incentives for each individual to defect.

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The Prisoner's Dilemma Quiz

Problem	Answer
What is the basic setup of The Prisoner's Dilemma?	Two prisoners are given the option to confess or stay silent, and their sentences depend on their individual and joint decisions.
In The Prisoner's Dilemma, what is the dominant strategy for each prisoner?	To confess, regardless of the other player's decision.
What is the outcome when both players confess in The Prisoner's Dilemma?	Both players receive a high sentence.
What is the outcome when both players stay silent in The Prisoner's Dilemma?	Both players receive a low sentence.
What is the outcome when one player confesses and the other stays silent in The Prisoner's Dilemma?	The player that confesses receives the lowest sentence possible, while the other player receives the highest sentence possible.
How does The Prisoner's Dilemma demonstrate the tension between individual and collective interests?	While both players would benefit from staying silent, the individual benefit of confessing outweighs the collective benefit of mutual silence.
How does The Prisoner's Dilemma relate to real-world situations, such as business or international relations?	It illustrates the importance of trust and cooperation, as well as the danger of competition and mistrust.
What is one strategy that has been proposed for solving The Prisoner's Dilemma?	Repeated play and communication, allowing for the establishment of trust and the possibility of future payoff.
How does the concept of the shadow of the future relate to The Prisoner's Dilemma?	It suggests that players' decisions are influenced by the potential long-term consequences of their actions, rather than just the immediate payoff.
What is the difference between the one-shot and iterated versions of The Prisoner's Dilemma?	In the one-shot game, players only play once and have no ability to communicate or establish trust. In the iterated game, players play multiple times and have the opportunity to learn from previous rounds and potentially establish a cooperative relationship.

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The Prisoner's Dilemma

Introduction

The prisoner's dilemma is a classic problem in game theory that models situations where individuals or groups make decisions that affect both themselves and others. It is a simple yet powerful tool for understanding the dynamics of cooperation and competition in social situations.

Key Concepts

Two players have the choice to either cooperate or defect.
The payoff of each player is dependent on their own choice and the choice of the other player.
The optimal strategy for each player depends on the other player's strategy.
The Nash equilibrium for the game is when both players defect, even though this is not the Pareto optimal solution.

Example

Two prisoners are caught and given separate cells, with no means of communicating with each other. The prosecutor offers each of them a deal: - If one confesses and the other remains silent, the confessor will go free and the other will get a 10-year sentence. - If both remain silent, they will each get a 1-year sentence. - If both confess, they will each get a 5-year sentence.

Analysis

In this scenario, the Nash equilibrium is for both prisoners to confess, even though it is not the optimal solution (if both remained silent, they would both have only received a 1-year sentence each).

Application

The prisoner's dilemma has many real-life applications, including: - Arms race between countries - Business competition - Environmental pollution

Takeaways

Always consider the impact of your actions on others, as their actions will impact you.
Cooperation and communication can lead to better outcomes for all parties involved.
The Nash equilibrium may not always be the best solution, and it is important to consider alternatives.

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Practice Sheet: The Prisoner's Dilemma

Instructions: Read each scenario and choose the best strategy for each player.

Scenario: Two criminals, Alice and Bob, have been arrested but the police are unable to convict them of a more serious crime. The police offer each criminal a plea bargain (individual offer) and give the following instructions:

- If one criminal accepts the plea deal and the other doesn't, the one who accepts will get a lighter sentence (6 years), while the other will get a heavy sentence (10 years).
- If both choose to accept the plea deal, both criminals will get a lighter sentence (8 years).
- If neither accepts the plea deal, both criminals will get a medium sentence (9 years).

What should Alice and Bob do?

Scenario: Two car manufacturers, Tesla and Ford, are planning to launch electric vehicles. They can decide between two strategies:

- **Cooperate:** Both companies launch an electric vehicle at a reasonable price, and each of them will get a share of profit.
- **Defect:** One company launches a high-quality electric vehicle, while the other launches a cheaper one. The company that launches the high-quality vehicle will get a bigger share of the profit, while the other company will get a smaller share.

What should Tesla and Ford do?

Scenario: Two countries, USA and China, are contemplating reducing their carbon emissions. They can decide between two strategies:

- **Cooperate:** Both countries will reduce their carbon emissions by 20%, and hence reduce the global carbon footprint.
- **Defect:** One country (USA) decides to reduce its carbon emissions while the other (China) continues to emit carbon gases as before. The country that reduces its carbon emissions will suffer more economic loss compared to the country that continues to emit carbon gases.

What should USA and China do?

Scenario: Two coffee shops, Starbucks and Dunkin Donuts, are competing to gain more customers. They can decide between two strategies:

- **Cooperate:** Both coffee shops can charge a lower price for a cup of coffee, and hence attract more customers to buy coffee.
- **Defect:** One coffee shop (Starbucks) decides to charge a higher price for a cup of coffee compared to the other (Dunkin Donuts). The coffee shop that charges a higher price will earn more profit, but the number of customers will decrease.

What should Starbucks and Dunkin Donuts do?

Scenario: Two cybersecurity firms, Secure Systems and Stealthy Security, can either cooperate or defect with respect to bidding on a project. They can either:

- **Cooperate:** Bid on the project, but not aggressively. If one of the firms wins the project, both firms share profits equally.
- **Defect:** Bid aggressively to secure the project. The firm that wins the project walks away with much more profit, and the other firm gets no profit.

What should Secure Systems and Stealthy Security do?

Scenario: Two friends, A and B, are planning to attend a concert. They can decide between two strategies:

- **Cooperate:** Both will attend the concert together, and hence enjoy the concert together.
- **Defect:** One friend decides to attend a different concert, while the other attends the concert alone. The friend who attends a different concert will have more entertainment, while the other friend will feel lonely.

What should A and B do?