For my dissertation I recently have been reading a lot from the evolutionary biology literature. These guys have done much very interesting work on cooperation.
Martin Nowak and Robert May wrote an interesting paper in 1992. What they did is to play the famous Prisoners’ Dilemma spatially. Yep, indeed interesting, because my dissertation is about migration and cooperation. In brief, they put the players on a lattice; assign different starting conditions (different payoffs, different number of cooperators and defectors in society, etc.), run the computer software and see what happens from one generation to the next when the players interact with each other. What they get is chaotically changing spatial patterns!
The figures below are not Persian rugs, but illustrate the presence of cooperators and defectors in a society for one generation, and the change from one generation to the next. Blue is a cooperator that was also a cooperator the preceding generation, Red is a defector that was also a defector, Yellow is a defector that was a cooperator, and Green is a defector that was a defector.
Martin Nowak and Robert May wrote an interesting paper in 1992. What they did is to play the famous Prisoners’ Dilemma spatially. Yep, indeed interesting, because my dissertation is about migration and cooperation. In brief, they put the players on a lattice; assign different starting conditions (different payoffs, different number of cooperators and defectors in society, etc.), run the computer software and see what happens from one generation to the next when the players interact with each other. What they get is chaotically changing spatial patterns!
The figures below are not Persian rugs, but illustrate the presence of cooperators and defectors in a society for one generation, and the change from one generation to the next. Blue is a cooperator that was also a cooperator the preceding generation, Red is a defector that was also a defector, Yellow is a defector that was a cooperator, and Green is a defector that was a defector.
Figures 1 and 2 are societies on a 200x200 lattice after 200 generations that started with 10% cooperators, 90% defectors. The difference in starting conditions is the advantage for defectors over cooperators.
Fig 1.
Fig 2.
Figure 3 and 4 are societies on a 99x99 lattice that started with a single defector at the center. The difference is that the snapshot of society is taken at different points in time. Nowak and May show that one gets an almost infinite sequence of different patterns. Also, because the rules of the game are symmetrical, the symmetry is maintained.
Fig 3. After 219 generations.
Fig 4. After 221 generations.Reference:Martin A. Nowak. Robert M. May. Evolutionary Games and Spatial Chaos. Nature. Vol. 359. 29 October 1992.
Being curious and interested in the above for my dissertation, I had a chat with Yair Ghitza - friend, colleague but also our Columbia University's Political Science Department's master coder. Not only did he explain me how to code up the above, within 50 minutes he had actually written the complete computer code in R that does exactly what happens in Nowak and May's paper. Of course we have a lot of ideas on how to build on Nowak and May's work, so: more to come!
ReplyDeleteI don't know whether these social system simulations tell something useful outside the lab.
ReplyDeleteHuberman, B. A., N. S. Glance. 1993. Evolutionary games and com-
puter simulations. Proc. Natl. Acad. Sci. USA 90(16) 7716–7718.
. For Nowak and May's response to Huberman and Glance,
ReplyDeletesee Nowak, Bonhoeffer and May, Proc NAS (USA) v91
pp4877-4881, May 1994.