Happy Independence Day! To celebrate our nation’s founding, my family and I often hit up the Cape. This year was no exception, there’s little to report. The weather has been spotty: a little rain here, a few showers there, but nothing substantial. Someone was playing bagpipes the other night. And I witnessed a gruesome car accident a few feet from my balcony during the fireworks spectacular. A mass of people immediately sprang up to help the man, direct traffic, and call 911 repeatedly until emergency vehicles could make their way here. I was genuinely impressed by the response, professional and make-shift alike. Within seconds the response team had the guy off to the hospital in no time flat. I think it prudent not to speculate on the cyclist’s health. I don’t want to jinx anything, you know.
And since it’s vacation time, I’m here, at the kitchen table, on my laptop, implementing genetic algorithms. Maybe later I’ll describe what I did. Maybe if I do, someone will be able to tell me if my results make any sense. Whether or not my programs reproduce the classical results isn’t really the point, though. Look at the evolution of strategies for playing the iterated prisoner’s dilemma: they make perfect modern art tile mosaics! I bet someone’d love to have this pattern on their pool floor or garden wall. (Don’t be alarmed that they don’t appear all that related. Each row in black represents the fittest individual from one of a number of independent runs. That is, they probably never had the chance to meet each other.) Imagine the graphic tastefully obscured by flowering vines. (Click on it for a larger image.)
I can see an upside-down raccoon in it. What can you find?
i love it joshy! i think maxwell dworkin needs a new wallprint scheme…
this shows less learning than my intuition expected. oh how i hope we’re on each other’s editorial boards for our respective future journal submissions…
Actually, the algorithm demonstrated a lot of learning. If you want, I can send you an individual run. Then the relatedness is much more apparent. The fact that the fitness landscape is dynamic means that the fittest individuals that rise to power changes from run to run. Pretend the earth got destroyed twenty-something times. Evolution starts over each time, working its magic on a brand new randomly created population.
I think it is known that no single strategy dominates in a finite PD tournament. In fact, you can see this qualitatively in my visualization above. That’s what makes the PD so tricky. In a finite tournament, there’s nothing to converge to. Instead, populations go through cycles. In the infinite case, Tit-for-Tat always wins. Check me on that, though. Nowak has some better strategies for finite tournaments. I’m only starting to get in the literature right now. Check back with me in a few weeks.