Game Theory Overview

Game Theory Focus

• The study of strategic decision-making in situations where multiple players interact.
• Emphasizes how players' choices influence the outcomes for both themselves and their opponents.

Game Theory Concepts

• Rationality: Players are assumed to act in their self-interest, seeking to maximize their gains.
• Information: Players may have complete, incomplete, or perfect information about the game and their opponents' strategies.
• Payoffs: The outcomes of each player's choices, expressed numerically or in other measurable terms.
• Strategies: The plans of action that players choose to employ.
• Equilibrium: A state where no player can improve their outcome by unilaterally changing their strategy, assuming the other players' strategies remain the same.

Player Strategy Definition

• A complete plan of action that specifies what a player will do in every possible circumstance of the game.

Dominant Strategy

• A strategy that yields the best outcome for a player regardless of the strategies chosen by other players.

Prisoner's Dilemma

• Two suspects are arrested for a crime.
• Each suspect is offered a deal: confess and implicate the other, or stay silent.
• The suspects are held in separate cells and cannot communicate.
• Outcomes:
  • If both confess, they both receive a moderate sentence.
  • If both stay silent, they both receive a light sentence.
  • If one confesses and the other stays silent, the confessor goes free, and the silent suspect receives a harsh sentence.
• Rationality: If each individual acts in their own self-interest, they will choose to confess, as they are better off even if their partner remains silent.
• Dilemma: The optimal outcome for both players is for them to stay silent. However, because they cannot communicate and fear the worst-case scenario, they both end up confessing and receive a worse outcome.