(5) How to outsmart the Prisoner’s Dilemma - Lucas Husted

The Scenario

• Characters: Two gingerbread men, Crispy and Chewy, confronted by a fox.

• Test: Each must choose whether to spare or sacrifice the other without knowing the other's choice.

Outcomes of Choices

• Both spare: Fox eats one limb from each.

• One spares, one sacrifices: Sparing gingerbread man is fully eaten, traitor keeps all limbs.

• Both sacrifice: Fox eats three limbs from each.

Game Theory Context

• This scenario represents the Prisoner's Dilemma.

• The analysis of their outcomes leads both to betray each other since it guarantees a better outcome irrespective of the other's decision.

• The strategy of mutual sacrifice is referred to as Nash Equilibrium.

Infinite Prisoner's Dilemma

• Following the betrayal, a wizard alters the scenario to repeat indefinitely.

• New Strategy: Both could agree to spare each other daily to maximize limb retention in the long run.

• Retaliation: If one chooses to sacrifice, the other will always choose to sacrifice afterwards.

Future Consideration and Delta

• Discounting Future: The gingerbread men may value future limbs less than current ones.

• Delta Value: Represents the degree to which future limbs are valued (0 = no value, 1 = full value).

• Mathematical Model: As long as delta is at least 1/3, it is mutually beneficial for the gingerbread men to cooperate and spare each other.

Real-Life Implications

• The analysis is comparable to real-world scenarios like trade negotiations and politics.

• Leaders often face similar dilemmas where today’s decisions influence future interactions.

• Conclusion: Rational cooperation, while difficult, can yield better results than selfish choices.