The Prisoners Dilemma Understanding Game Theory A nonzerosum
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The Prisoner’s Dilemma Understanding Game Theory A non-zero-sum game
What is the prisoner’s dilemma? • Here is the scenario: • Game of “chicken” –two people driving cars toward each other Swerve Don’t swerve Swerve (keep car, keep car) (lose car, win car) Don’t swerve (win car, lose car) (lose car, lose car) • What would you do?
Let’s Play A Game! • You and your accomplice have robbed the American Museum of Natural History for its most prized fossil possessions and you have been apprehended!!! • Here is the scoop: • No enough evidence for conviction…. • You are questioned independently and offered the same deal
Your choices and consequences Prisoner B remains silent Prisoner B defects Prisoner A remains silent Both get 5 A gets 0, B gets 10 Prisoner A defects A gets 10, B gets 0 Both get 1 10 rounds: (record the result for each round ) • Pair up, independently write down “S” or “D”, then show each other the choice • Write down points for each round • Switch partners • Most points “win” the game!
Extension Questions • How does this activity illustrate the relationship between behavior and survival? • What strategy seems to be the best fit for the prisoner’s individual survival? • What strategy seems to be best fit for the survival of a population of individuals?
Animal Behavior and Game Theory • In Game Theory Individual wants to maximize his/her own returns. • In biology, the “return” we speak of is really the concept of fitness. • Essential Question: If natural selection is “survival of the fittest, ” then under what conditions should individuals engage aggressively in conflict for limited resources? Can aggressive and non-aggressive strategies coexist?
Frequency dependent selection • Frequency dependent selection occurs when the fitness of an individual depends on the relative frequency of other phenotypes in the population. • Positive frequency dependent selection – majority advantage (majority phenotype wins). • Negative frequency dependent selection – minority advantage. Promotes genotypic and phenotypic diversity. Some combination of phenotype. • Frequencies may exist at which all phenotypes have the same fitness. 7
