Game Theory Chapter 3 Quiz

Sequential Games

• First-mover advantage allows the first player to influence the game outcome to their preference.
• Last-mover advantage enables the last player to finalize the game in their favor.

Nash Equilibrium in Simultaneous Games

• In a game with two players choosing between strategies A and B, the outcomes are:
  • Both choose A: Payoff of 3 each.
  • Player 1 chooses A, Player 2 chooses B: Payoff of 1 for Player 1, 0 for Player 2.
  • Player 1 chooses B, Player 2 chooses A: Payoff of 3 for Player 2, 1 for Player 1.
  • Both choose B: Payoff of 2 for Player 1, 0 for Player 2.
• Player 2's Nash Equilibrium payoff is 3 when both players choose A.

Group Project Cooperation Scenario

• Four students can either cooperate or defect; success requires all to cooperate.
• Cost of cooperation is 10; successful project payoff is 9, failure results in 0.
• Nash equilibrium occurs when all students defect since cooperating leads to a guaranteed loss of payoff.

Definitions

• Nash Equilibrium: A condition where each participant in a game chooses the best strategy given the choices of others, ensuring no incentive to deviate.
• Pareto Efficiency: An outcome where no player can be made better off without making another player worse off.

Analysis of Group Project Outcomes

• Given the cooperation cost exceeds potential payoff, the optimal strategy for all is to defect resulting in a guaranteed payoff of 0.
• This point highlights that cooperation does not lead to a better payoff compared to non-cooperation.

Tit-for-Tat Strategy

• Most effective in repeated interactions that are open-ended, fostering a cooperative environment.

Subgame Perfect Nash Equilibrium

• Equilibrium A contains non-credible threats, making it less reliable in game strategy context.
• Equilibrium B maintains no non-credible threats, thereby qualifying as a Subgame Perfect Nash Equilibrium.