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MrMind comments on Inefficient Games - Less Wrong Discussion

14 Post author: capybaralet 23 August 2016 05:47PM

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Comment author: Gram_Stone 23 August 2016 07:15:56PM *  13 points [-]

It's nice to see that someone else has thought about this.

It's a popular rationalist pastime to try coming up with munchkin solutions to social dilemmas. A friend posed one such munchkin solution to me, and I thought he had an unrealistic idea of why regulations work, so I said to him:

Even though it's what you really want, I don't think the fact that you know everyone else will cooperate is the interesting thing per se about regulations, but that this is a consequence of the fact that you have decreased what was once the temptation payoff and thus constructed a different game. You have functionally reduced the expected payoff of the option "Don't pay taxes," by law. If you don't pay taxes, then you get fined or jailed. Now all players are playing a game where the Nash equilibrium is also Pareto optimal: Pay taxes or be fined or jailed. Clearly, one should pay taxes.

Now, ironically, this is good news if we want to cause better outcomes with less or no coercion, because it suggests that it is not coercion in itself that does the good work, but the fact that we have changed the payoffs to construct a different game; we can interpret coercion as just one instantiation of the general process by which 'inefficient games' become 'efficient games'. Coercion is perhaps a simple way to do the thing that all possible solutions to this problem seem to have in common, but there may be others that we can assume to syntactically change the payoffs in the way that coercion does, but which we may semantically interpret as something other than coercion.

A different time, a friend noticed that people building up trust seemed qualitatively similar to a Prisoner's Dilemma but couldn't see exactly how. I was like, "Have you heard of Stag Hunt? That's the whole reason Rousseau came up with it!" PD is just one kind of coordination game.

More generally, isn't it weird that the central objects of study in game theory, despite all of the formalization that has taken place since the beginning of the field, are remembered in the form of anecdotes?! You learn about the Stag Hunt and the Prisoner's Dilemma and Chicken and all other sorts of game, but there doesn't really seem to be any systematic notion of how different games are connected, or if any games are 'closer' to others in some sense (as our intuitions might suggest).

Meditations on Moloch was pretty but in the audience I coughed the words 'mechanism design'. It just seems like pointing out the mainstream academic work makes you boring when you're commenting on something poetic. You also might like Robinson and Goforth's Topology of the 2x2 Games. The math isn't that complex and it provides more insight than a barrage of anecdotes. Note that to my knowledge this is not taught in traditional game theory courses but probably should be one day. They refer to this general class of games as the 'social dilemmas', if I recall correctly.

Comment author: MrMind 30 August 2016 09:46:00AM *  2 points [-]

Gram, may I hijack your expertise? Game theory is something that I've always wanted to study formally. Can you recommend me some sources to learn about things like mechanism design?

Comment author: Gram_Stone 30 August 2016 04:37:05PM 5 points [-]

I'm certainly not an expert, but I'll try to give some advice.

For game theory proper there's Yvain's sequence (and Schelling's book, which it's based off of) and/or Tadelis's Game Theory.

A good way to get to mechanism design might be through introductory economics and auction theory. McAfee's Introduction to Economic Analysis is an open econ textbook, good for people with a solid understanding of basic calculus. It assumes this bit of math so that the presentation is a lot shorter and more elegant. (Apostol is my calculus textbook of choice. If you've never done math where you actually have to prove things, then Velleman's How to Prove It will get you started. If you can't prove then you're just memorizing passwords. It's easier than it seems at first.) After IEA, Krishna's Auction Theory will segue from basic auction theory to basic mechanism design. Haven't gotten much further than that.

There's also a mechanism design sequence on LW. I haven't looked at it too closely and it might move too quickly for someone without the right background.

Comment author: MrMind 31 August 2016 07:27:01AM *  2 points [-]

This is an awesome answer, thank you very much!

IEA is also a favourite of mine.