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The Iterated Prisoner ‘ s Dilemma

This work delves into the Iterated Prisoner's Dilemma (IPD) and its relevance to social cooperation and competition. It examines key concepts such as mutual aid, adaptive dynamics, and various strategies like Tit-for-Tat and Win-Stay Lose-Shift. The relationship between individual interests and societal benefits, as discussed by thinkers like Adam Smith and Joseph Stiglitz, is highlighted. The study also considers the influence of errors and memory on strategy effectiveness, exploring both mathematical frameworks and evolutionary dynamics in the context of cooperation.

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The Iterated Prisoner ‘ s Dilemma

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  1. The Iterated Prisoner‘s Dilemma

  2. Darwin: The small strength and speed of man, his want of natural weapons, etc., are more than counterbalanced ... by his social qualities, which led him to give and receive aid from his fellow men.

  3. Mutual aid

  4. The one-shot PD

  5. Adam Smith (1723-1790) • …by pursuing his own interest, man frequently promotes that of the society more effectually than when he really intends to promote it…

  6. Adam Smith: Man intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention. Joseph Stiglitz: The reason that the invisible hand often seems invisible is that it is often not there.

  7. Payoff for repeated games

  8. The Good, the Bad and the Discriminator • ALLC • ALLD • TFT • frequencies x,y,z (x+y+z=1)

  9. Payoff matrix

  10. Replicator Dynamics

  11. Replicator Dynamics

  12. IPD with errors

  13. IPD with errors

  14. IPD with errors

  15. IPD

  16. Evolving Generosity

  17. Reacting on co-player

  18. The iterated Prisoner´s Dilemma

  19. The iterated Prisoner´s Dilemma

  20. The iterated Prisoner´s Dilemma

  21. The iterated Prisoner´s Dilemma

  22. The iterated Prisoner´s Dilemma

  23. The iterated Prisoner´s Dilemma

  24. Adaptive Dynamics

  25. Adaptive Dynamics

  26. Adaptive Dynamics

  27. Adaptive Dynamics

  28. Adaptive Dynamics for the IPD

  29. Adaptive Dynamics for the IPD

  30. Adaptive Dynamics for the IPD

  31. Adaptive Dynamics for the IPD

  32. Reacting on last round

  33. Reacting on last round

  34. The fearsome four • Heteroclinic network • A = Tit or Tat • B = Firm But Fair • C = Bully • D = ALLD

  35. …and the winner is…

  36. Win-Stay. Lose-Shift WSLS

  37. WSLS

  38. WSLS

  39. Win-Stay, Lose-Shift WSLS • Simple learning rule • stable, error-correcting • but needs retaliator to prepare the ground

  40. Memory-one strategies

  41. Memory-one strategies

  42. A new breath: Press and Dyson PNAS 2012 AMS homepage (‚Maths in the Media‘) ‚The world of game theory is currently on fire...‘ ‚this is a monumental surprise...‘ ‚the emerging revolution of game theory...‘

  43. Dyson‘s formula

  44. Zero-determinant (ZD) strategies

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