Game Theory Overview and Prisoner's Dilemma

Game Theory Overview

• Game theory is a framework for studying strategic interactions among rational agents.
• Static games of complete information involve simultaneous decisions, with players knowing the possible actions and outcomes.

Prisoner's Dilemma

• Two suspects face a choice: confess or deny a crime.
• If both deny, they are each sentenced to one month in jail.
• If both confess, they are each sentenced to six months.
• If one confesses and the other denies, the confessor is released, and the denier receives a longer sentence.

Prisoner's Dilemma in Normal Form

• The game is represented as a payoff matrix.
  • Rows represent the strategies of one player, columns represent the strategies of the other.
  • Payoffs are shown for each combination of strategies.

Equilibrium and Dominant Strategies

• A rational player won't play a strictly dominated strategy (a strategy that's always worse than another).
• Confessing is a dominant strategy in the Prisoner's Dilemma because it's the better option regardless of the other player's choice.
• The outcome where both players confess is the Nash Equilibrium.

Equilibrium and Dominant Strategies

• The strategy "Deny" is strictly dominated by the strategy "Confess," and the opposite is true, "Confess" is a dominant strategy.
• Nash equilibrium is where both players choose the dominant strategy, despite the fact that it yields a worse outcome for both than if they had both denied.

Equilibrium and Dominant Strategies (continued)

• Not all games have a strictly dominated strategy
• All possible combinations of outcomes become possible equilibria in such a game.

Best Responses

• A rational player chooses the best response given their beliefs about the actions of other players.

Nash Equilibrium

• A Nash equilibrium is a situation where each player's strategy is the best response to the strategies of all other players.
• Strategy pairs that fail to meet this condition are not considered plausible outcomes.

A Cooperation Game

• A simple example demonstrating strategic interactions requiring cooperation for optimal results.
• Shows the importance of cooperation and potential for mutual benefit through cooperative choices

Battle of the Sexes

• A game where two players prefer to be together but disagree on what to do together.
• There are multiple Nash equilibria, demonstrating multiple possible outcomes driven by individual preferences.

Stag Hunt

• A game highlighting the tension between individual incentives and collective action.
• Both players must choose the same action for one optimal outcome, but each has an incentive to choose a suboptimal outcome when faced with uncertainty or fear.
• Shows how cooperation can lead to better outcomes but is challenging to achieve.

Focal Points

• Focal points are specific strategy combinations that stand out, aiding coordination and cooperation in strategic interactions.

Strict and Non-Strict Equilibria

• Strict Nash Equilibria exist where a deviation always results in a worse outcome for the player pursuing the deviation.
• The concept of Nash Equilibrium only requires that a deviation does not result in a better outcome for the deviating player.