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Mathematical models of human cooperation - Matjaž Perc

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Let’s face complexity September 4-8, 2017

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Mathematical models of human cooperation - Matjaž Perc

  1. 1. Mathematical models of human cooperation Matjaž Perc Let’s Face Complexity: New Bridges Between Physical and Social Sciences Como, September 2017 Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia CAMTP - Center for Applied Mathematics and Theoretical Physics, University of Maribor, Slovenia Complexity Science Hub, Vienna, Austria
  2. 2. Mathematical models of human cooperation Matjaž Perc http://www.matjazperc.com/ matjazperc@gmail.com
  3. 3. Mathematical models of human cooperation Matjaž Perc http://www.matjazperc.com/ matjazperc@gmail.com
  4. 4. Mathematical models of human cooperation
  5. 5. Mathematical models of human cooperation
  6. 6. Mathematical models of human cooperation
  7. 7. Mathematical models of human cooperation The theoretical framework is evolutionary game theory: Players play simple games that capture the essence of the problem. The essence of the problem is that human cooperation is a social dilemma! This means that individual best interests are at odds with what is best for the society as a whole. Essentially, we have a struggle between Darwinian principles and our pro-social drive.
  8. 8. Mathematical models of human cooperation
  9. 9. Mathematical models of human cooperation Public goods game on the square lattice as the null model
  10. 10. Mathematical models of human cooperation Public goods game on the square lattice as the null model s. Rev. E 80, 056109 (2009)
  11. 11. Mathematical models of human cooperation Public goods game on the square lattice as the null model
  12. 12. Mathematical models of human cooperation Public goods game on the square lattice(?) as the null model s. Rev. E 80, 056109 (2009)
  13. 13. Which network to choose? And why?
  14. 14. Which network to choose? And why?
  15. 15. Public goods game on the square lattice + punishment R=3.8
  16. 16. Public goods game on the square lattice + reward R=3.5
  17. 17. Public goods game on the square lattice + reward R=3.5 R=2.0
  18. 18. Public goods game on the square lattice + both R=2.5
  19. 19. Public goods game on the square lattice + both R=2.5
  20. 20. Public goods game on the square lattice + both R=2.5 R=4.5
  21. 21. Public goods game on the square lattice + both R=4.5
  22. 22. Public goods game on a square lattice + both
  23. 23. Public goods game on the square lattice + tolerance
  24. 24. Public goods game on the square lattice + tolerance
  25. 25. Public goods game on the square lattice + tolerance
  26. 26. Stability of subsystem solutions 8 strategies 4 strategies 15 subsystem solutions, 105 pairs in a round-robin tournament 255 subsystem solutions, 32385 pairs in a round-robin tournament
  27. 27. Public goods game on the square lattice + tolerance
  28. 28. Public goods game on the square lattice + tolerance
  29. 29. Stability of subsystem solutions
  30. 30. Stability of subsystem solutions
  31. 31. Fast MC simulation of agent-based models “double tilling decomposition” Eur. J. Phys. 38, 045801 (2017)
  32. 32. Fast MC simulation of agent-based models
  33. 33. Fast MC simulation of agent-based models
  34. 34. Mathematical models of human cooperation

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