Inefficient Games

by capybaralet1 min read23rd Aug 201613 comments


Personal Blog

There are several well-known games in which the pareto optima and Nash equilibria are disjoint sets.
The most famous is probably the prisoner's dilemma.  Races to the bottom or tragedies of the commons typically have this feature as well.

I proposed calling these inefficient games.  More generally, games where the sets of pareto optima and Nash equilibria are distinct (but not disjoint), such as a stag hunt could be called potentially inefficient games.

It seems worthwhile to study (potentially) inefficient games as a class and see what can be discovered about them, but I don't know of any such work (pointers welcome!)

13 comments, sorted by Highlighting new comments since Today at 9:16 PM
New Comment

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.

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?

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.

This is an awesome answer, thank you very much!

IEA is also a favourite of mine.

I wish it were more widely understood that the groups who agitate to have regulations placed on certain industries are often composed of the participants of those industries, not outsiders trying to arbitrarily place shackles on them. Companies want to construct a better game where the optimal choice for them and their competitors is one that doesn't destroy value.

Companies want to construct a better game where the optimal choice for them and their competitors is one that doesn't destroy value.

Didn't you mean to write

Companies want to construct a better game where they get more profitable and doing business is hard for the competitors.


I think they want both.

In the oil industry, it is in no one's interest that there be any uncertainty or vagueness in the regulations about what should be considered a "bookable reserve" which a company can formally count as part of its net assets. Everyone wants the definitions to be extremely clear because then investors can make decisions with confidence and clarity, more money flows through the system, and assets can be traded and sold easily.

A world without such regulations is worse for everyone, except perhaps the extremely skilled con artist, and even those people have to live in a system with less net cash flowing through it due to the aforementioned uncertainty.

On the net, if a company can lobby for a regulation that increases their profits, they will do so regardless of whether that regulation also creates profits for their competitors.

If possible, of course, they will select regulations that preferentially favor their own company. I'm sure this is very widespread. But it isn't the only use of regulation.

Well, yes, but your example is a sub-type of my "more profitable" claim. The companies want the definitions to be clear because otherwise there is a large uncertainty cost which will affect profits. They don't care about destroying value as long as it's not their value.

I agree that companies often lobby for regulations which decrease their risk -- but typically what they want is to ossify the existing structures and put up barriers to newcomers and outside innovation. If you are large and powerful enough to influence regulations, you want to preserve your position as large and powerful. Generally speaking, that's not a good thing.

In this case, we should really define "coercion". Could you please elaborate what you meant through that word?

One could argue, that if someone holds a gun to your head and demands your money, it's not coercion, just a game, where the expected payoff of not giving the money is smaller than the expected payoff of handing it over.

(Of course, I completely agree with your explanation about taxes. It's just the usage of "coercion" in the rest of your comment which seems a little odd)

I do not think that Gram_Stone is making the claim that fining or jailing those who do not pay their taxes is not coercion. Instead, I think that he is arguing that it is not the coercion per se that results in most people paying their taxes, but rather that (due to the coercion) failing to pay taxes does not have a favorable payoff, and that it is the unfavorable payoff that causes most people to pay their taxes. So, if there were some way to create favorable payoffs for desirable behavior without coercion, then this would work just as well as does using coercion.

Gram_Stone, please correct me if that is not accurate. Also, do you have any ideas as to how to make voluntary payment of taxes have a favorable payoff without using coercion?

That sounds accurate to me.

I can't think of anything off of the top of my head. I was really just trying to point out the general dynamic.

I originally used 'fiat' instead of 'coercion'. I was just trying to make sure we don't miss other possibilities besides regulations for solving problems like these.

I thought that PD and "stag hunt" were standard names for these classes, but I generally prefer description ("inefficient") over metonymy. Maybe "perverse incentive game" or "antisocial game"?