Let’s face complexity September 4-8, 2017

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. Mathematical models of
human cooperation
Matjaž Perc
http://www.matjazperc.com/
matjazperc@gmail.com

3. Mathematical models of
human cooperation
Matjaž Perc
http://www.matjazperc.com/
matjazperc@gmail.com

4. Mathematical models of
human cooperation

5. Mathematical models of
human cooperation

6. Mathematical models of
human cooperation

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. Mathematical models of
human cooperation

9. Mathematical models of
human cooperation
Public goods game on the square lattice as the null model

10. Mathematical models of
human cooperation
Public goods game on the square lattice as the null model
s. Rev. E 80, 056109 (2009)

11. Mathematical models of
human cooperation
Public goods game on the square lattice as the null model

12. Mathematical models of
human cooperation
Public goods game on the square lattice(?)
as the null model
s. Rev. E 80, 056109 (2009)

13. Which network to choose?
And why?

14. Which network to choose?
And why?

15. Public goods game on the square lattice + punishment
R=3.8

16. Public goods game on the square lattice + reward
R=3.5

17. Public goods game on the square lattice + reward
R=3.5 R=2.0

18. Public goods game on the square lattice + both
R=2.5

19. Public goods game on the square lattice + both
R=2.5

20. Public goods game on the square lattice + both
R=2.5 R=4.5

21. Public goods game on the square lattice + both
R=4.5

22. Public goods game on a square lattice + both

23. Public goods game on the square lattice + tolerance

24. Public goods game on the square lattice + tolerance

25. Public goods game on the square lattice + tolerance

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. Public goods game on the square lattice + tolerance

28. Public goods game on the square lattice + tolerance

29. Stability of subsystem solutions

30. Stability of subsystem solutions

31. Fast MC simulation of agent-based models
“double tilling decomposition”
Eur. J. Phys. 38, 045801 (2017)

32. Fast MC simulation of agent-based models

33. Fast MC simulation of agent-based models

38. Mathematical models of
human cooperation