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Game Theory 101 (#2): The Prisoner's Dilemma and Strict Dominance
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Game Theory 101 (#2): The Prisoner's Dilemma and Strict Dominance

Introduction to the Prisoner's Dilemma and Strict Dominance Solution Concept

In this section, William Spaniel introduces the concept of the prisoner's dilemma and explains how it relates to game theory. He also discusses the strict dominance solution concept.

The Prisoner's Dilemma

  • The situation involves two suspects who are arrested by the police.
  • The police have evidence of trespassing but need a confession for a greater crime.
  • The suspects are placed in separate interrogation rooms and offered a deal.
  • If both keep quiet, they will be charged with trespassing (1 month in jail each).
  • If one confesses and the other doesn't, the confessor goes free while the other gets 12 months in jail.
  • If both confess, they will be punished for robbery (8 months in jail each).

Payoff Matrix

  • A payoff matrix is used to represent the outcomes of different strategies.
  • In this case, there are two players (Player 1 and Player 2) with two strategies: confess or keep quiet.
  • If both keep quiet, they both spend 1 month in jail (-1 payoff).
  • If one confesses and the other keeps quiet, the confessor gets no time in jail while the other gets 12 months (-12 payoff).
  • If both confess, they both spend 8 months in jail (-8 payoff).

Strict Dominance Solution Concept

  • Player 1's strategy of confess strictly dominates their strategy of keeping quiet.
  • Regardless of what Player 2 does, Player 1 is always better off confessing.
  • Rational players never play strictly dominated strategies.

Conclusion and Solving the Prisoner's Dilemma

In this section, William Spaniel concludes his explanation of the prisoner's dilemma and discusses how to solve it.

Solving the Prisoner's Dilemma

  • Player 1 will always confess, as it strictly dominates keeping quiet.
  • To determine Player 2's strategy, consider what they would do if they knew Player 1 was going to keep quiet.
  • If Player 1 keeps quiet, Player 2 is better off confessing (0 payoff > -1 payoff).
  • Therefore, both players will confess in this game.

Final Thoughts

In this section, William Spaniel provides some final thoughts on the prisoner's dilemma and rational player behavior.

Rational Player Behavior

  • Rational players never play strictly dominated strategies.
  • It doesn't make sense for them to choose a strategy that leads to a worse outcome when there is a better alternative available.
  • In future videos, players will not be playing strictly dominated strategies.

By understanding the concept of strict dominance and applying it to the prisoner's dilemma, we can analyze player behavior and predict their choices in various situations.

New Section Why is the outcome of both players keeping quiet not chosen?

In this section, the speaker explains why the outcome of both players keeping quiet is not chosen in the prisoner's dilemma game.

The Better Outcome for Both Players

  • The outcome of both players keeping quiet is mutually better for them collectively.
  • Confessing leads to a worse outcome individually and collectively (-1 and -1), compared to both players keeping quiet.

Lack of Stability in the Quiet Outcome

  • Each player can individually do better by switching to confess.
  • There isn't a stable solution because they can always switch their strategies to confess.
  • Agreements made before going into interrogation rooms don't withstand the test of time.
  • As soon as they are in the room, it becomes in their individual interest to confess rather than keep quiet.

Sensible Outcome: Both Players Confess

  • The only sensible outcome is when both players confess.
  • This is because it aligns with their individual interests to confess rather than keep quiet.
  • This scenario represents the prisoner's dilemma and strict dominance.

New Section Introduction to Strict Dominance

In this section, the speaker introduces strict dominance and how it can be used in game theory.

Understanding Strict Dominance

  • Strict dominance refers to a strategy that always yields a higher payoff regardless of what other players choose.
  • It helps identify dominant strategies that are optimal regardless of what others do.

Exploring Strict Dominance in Game Theory

  • The concept of strict dominance allows us to analyze different outcomes and determine which ones are more favorable based on individual interests.
  • By considering strict dominance, we can make predictions about player behavior and outcomes in various games.

The next video will delve deeper into how strict dominance can be applied.

Video description

Game Theory 101: The Complete Textbook on Amazon: https://www.amazon.com/Game-Theory-101-Complete-Textbook/dp/1492728152/ http://gametheory101.com/courses/game-theory-101/ Two prisoners are locked into separate interrogation rooms. The cops know they were trespassing and believe they were planning on robbing a store, but they lack sufficient evidence to charge them with the latter crime. Thus, they offer the prisoners the following deal: If no one confesses, both will only be charged with trespassing and receive a sentence of one month. If one confesses while the other keeps quiet, the confessor will get to walk away free, while the one who kept quiet will be charged to the fullest extent of the law--twelve months in jail. Finally, if both confess, each criminal's testimony is less useful, and both will be locked up for eight months. If each prisoner only want to minimize the amount of time he spends in jail, what should they do? This lesson introduces the concept of strict dominance, which is a very useful tool for a game theorist.