Epistemic Status: Common knowledge, just not to me

The Evolution of Trust is a deceptively friendly little interactive game. Near the end, there’s a “sandbox” evolutionary game theory simulator. It’s pretty flexible. You can do quick experiments in it without writing code. I highly recommend playing around.

One of the things that surprised me was a strategy the game calls Simpleton, also known in the literature as Pavlov. In certain conditions, it works pretty well — even better than tit-for-tat or tit-for-tat with forgiveness.

Let’s set the framework first. You have a Prisoner’s dilemma type game.

If both parties cooperate, they each get +2 points.
If one cooperates and the other defects, the defector gets +3 points and the cooperator gets -1 point
If both defect, both get 0 points.

This game is iterated — you’re randomly assigned to a partner and you play many rounds. Longer rounds reward more cooperative strategies; shorter rounds reward more defection.

It’s also evolutionary — you have a proportion of bots each playing their strategies, and after each round, the bots with the most points replicate and the bots with the least points die out. Successful strategies will tend to reproduce while unsuccessful ones die out. In other words, this is the Darwin Game.

Finally, it’s stochastic — there’s a small probability that any bot will make a mistake and cooperate or defect at random.

Now, how does Pavlov work?

Pavlov starts off cooperating. If the other player cooperates with Pavlov, Pavlov keeps doing whatever it’s doing, even if it was a mistake; if the other player defects, Pavlov switches its behavior, even if it was a mistake.

In other words, Pavlov:

cooperates when you cooperate with it, except by mistake
“pushes boundaries” and keeps defecting when you cooperate, until you retaliate
“concedes when punished” and cooperates after a defect/defect result
“retaliates against unprovoked aggression”, defecting if you defect on it while it cooperates.

If there’s any randomness, Pavlov is better at cooperating with itself than Tit-For-Tat. One accidental defection and two Tit-For-Tats are stuck in an eternal defect cycle, while Pavlov’s forgive each other and wind up back in a cooperate/cooperate pattern.

Moreover, Pavlov can exploit CooperateBot (if it defects by accident, it will keep greedily defecting against the hapless CooperateBot, while Tit-For-Tat wil...

Alexander Genkin

Alexander Genkin

Alexander Genkin

Alexander Genkin