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Understanding Game Theory: Strategies, Payoff Matrices, and the Prisoner's Dilemma

This text explores complex game theory concepts, including the circumference of the Earth, hermaphroditic fish strategies, and altruistic behaviors in the Prisoner's Dilemma. Players in various scenarios must decide whether to demand preferred roles or accept either role, impacting their payoffs based on strategies chosen. The discussion extends to constructing payoff matrices, understanding Nash equilibria, and analyzing dominant strategies under different conditions, illustrating the interplay between individual preferences and collective outcomes in competitive environments.

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Understanding Game Theory: Strategies, Payoff Matrices, and the Prisoner's Dilemma

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Presentation Transcript

  1. Game Problems

  2. Which number is closest to the circumference of the earth? • 15,000 miles • 25,000 miles • 35,000 miles • 45,000 miles • 55,000 miles

  3. Hermaphroditic Fish: Ex 18.1 • Two players: Fish 1 and Fish 2 • Two strategies: • Demand preferred role • Accept either role • Payoffs • H if one gets to play preferred role • L if one plays less preferred role • S if no match

  4. Payoff matrix See Blackboard

  5. When is this game a prisoners’ dilemma? • For what values of H, L, and S is it a dominant strategy to demand preferred role? • Further question: Suppose S is the value of playing the same game with someone else at a later date. If everybody demands to play preferred role, how does S compare with L?

  6. Extension • What if tastes differ so that half of the population prefers role 1 and half prefers role 2? • Construct payoff matrix. • When is there a dominant strategy?

  7. Altruists Prisoners’ Dilemma: Ex 27.1 • Original game • What happens with altruists? • Try a=1 • For what values of a is this a Prisoners’ dilemma? Quiet Fink Quiet Fink

  8. Road Warriors X A 6,9,12,15 20,21,22,23 20,21,22,23 B 6.9,12,15 Y

  9. Nash equilibrium • Make table

  10. Road Warriors II A New Road X A 6,9,12,15 20,21,22,23 7,8,9,10 20,21,22,23 B 6.9,12,15 Y

  11. Domination Left Center Right Top Middle Bottom

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