[LINK] Prisoner's Dilemma? Not So Much

post by torekp · 2014-05-20T23:38:19.450Z · score: 4 (7 votes) · LW · GW · Legacy · 18 comments

Hannes Rusch argues that the Prisoner's Dilemma is best understood as merely one game of very many:

only 2 of the 726 combinatorially possible strategically unique ordinal 2x2 games have the detrimental characteristics of a PD and that the frequency of PD-type games in a space of games with random payoffs does not exceed about 3.5%. Although this does not compellingly imply that the relevance of PDs is overestimated, in the absence of convergent empirical information about the ancestral human social niche, this finding can be interpreted in favour of a rather neglected answer to the question of how the founding groups of human cooperation themselves came to cooperate: Behavioural and/or psychological mechanisms which evolved for other, possibly more frequent, social interaction situations might have been applied to PD-type dilemmas only later.



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comment by Manfred · 2014-05-21T20:18:48.531Z · score: 4 (4 votes) · LW(p) · GW(p)

Looks like they deliberately use a conservative formulation of the "detrimental characteristics of a PD." Both players are required to have a dominant strategy, that leads to a situation where both are worse off than the optimal square.

A more expansive formulation would be something like "there is a Nash equilibrium that is not Pareto optimal." If the preference-ranking version of the PD is something like [[11],[24]][[42],[33]], this means that we'd also notice something interesting about the game [[22],[14]][[41],[43]], etc.

comment by torekp · 2014-05-22T00:39:39.152Z · score: 4 (4 votes) · LW(p) · GW(p)

I find the narrow definition of "PD-type" games useful. You raise a good question though, to which the author's answer is

we find a total 34 (=4.68%) games which have a unique inefficient Nash-equilibrium.

comment by tut · 2014-06-03T16:10:27.745Z · score: 0 (0 votes) · LW(p) · GW(p)

there is a Nash equilibrium that is not Pareto optimal

Like Stag Hunt.

What they argue is that mechanisms for producing mutual cooperation in games like your more expansive formulation but that don't match the deliberately conservative formulation might have been important in the evolution of cooperativeness.

comment by satt · 2014-05-21T00:46:06.290Z · score: 3 (3 votes) · LW(p) · GW(p)

The analytic result (that only 2 of 736 strategically unique ordinal 2×2 games are PDs) is interesting, the numerical simulation less so; the paper doesn't motivate the specific choice of a uniform distribution from which to randomly sample payoffs. (I can imagine the results changing quite a lot if the payoffs are taken from e.g. lognormal or normal distributions instead.)

comment by torekp · 2014-05-25T16:07:39.974Z · score: 1 (1 votes) · LW(p) · GW(p)

Wanna bet? I made a few Prediction Book entries. The author was nice enough to give me his source code; I modified it and ran it. I will edit this comment as soon as I finish cranking out the results. I'll rot13 them, or hide them in a spoiler window (is that possible?), for those who'd like to try a Prediction Book probability estimate.

I neglected to make Prediction Book entries for the lognormal distribution, but they would have been similar. Herewith, the results in rot13:

Normal distribution: guerr cbvag sbhe creprag

Lognormal: guerr cbvag svir creprag

Additional edit: based on a few runs, the error of those estimates from the true mean is of the order of 0.1%.

comment by satt · 2014-05-25T19:44:01.722Z · score: 0 (0 votes) · LW(p) · GW(p)

I'd put, say, 45% on continuous normal distributions giving a <3.4% PD proportion, and 55% on them giving a ≤5.1% distribution. (I don't have a PredictionBook account so I'll just note those probabilities here before I look at your answers.)

Edit: I'll rot13 everything after this sentence in case anyone else is making guesses. V jnf jebat! Gur cerpvfr qvfgevohgvba nccrnef gb znxr ab qvssrerapr, cerfhznoyl orpnhfr gur CQ'f na beqvany curabzraba, abg n pneqvany bar. (Cerfhznoyl bar pbhyq cebir guvf zngurzngvpnyyl gb obyfgre Ehfpu'f cbvag.)

comment by John_Maxwell (John_Maxwell_IV) · 2014-05-21T00:37:49.588Z · score: 3 (3 votes) · LW(p) · GW(p)

Do we have reason to think that games where both players make their move simultaneously are more important than games where you get to see your opponent's move before you make yours, or other game structures?

comment by Jayson_Virissimo · 2014-05-21T05:48:03.041Z · score: 6 (6 votes) · LW(p) · GW(p)

My priors are that most important social situations are not best modeled as simultaneous games.

In a formal game, the player must make his move all the way, he is not allowed pauses, feints or tentative half-moves whose second half depends on the equally tentative reactions, tâtonnements of the other player. In the state of nature a player, before even making a half-move, may make speeches, brandish his weapon, cajole, etc. Depending on the other player's reaction or rather on his reading of it, he may walk away (if the other stands his ground), or strike a blow (either because the other looks about to strike first, or because he is looking the other way), or perhaps hear and consider an offer of Danegeld.

-- Anthony de Jasay, The State

comment by shminux · 2014-05-21T00:32:07.311Z · score: 2 (2 votes) · LW(p) · GW(p)

What caused the initial emergence of cooperative strategies in environments of PD-type?

I'd think that cooperative strategies emerge in non-PD-type situations, where individual defection is strictly worse than cooperation (e.g. hunting large prey in packs). When the environment changes toward PD-type (e.g. shortage of large prey means not every pack member is fed), some individuals evolve to defect. However, having too many of them results in reduced benefit for everyone, so the defection mutation never spreads too widely (e.g. a pack where everyone starts to defect by fighting and possibly killing others for food share soon becomes too small to hunt effectively). Instead of straight up defection, other mutations provide more fitness without significant detriment (e.g. pack hierarchy with the strongest thriving and the weakest dying out).

The summary you quoted seems to imply something like this. I am not familiar with the actual research on the topic, however, feel free to summarize.

comment by redlizard · 2014-05-21T06:29:12.059Z · score: 4 (6 votes) · LW(p) · GW(p)

Group selectionism alert. The "we are optimized for effectively playing the iterated prisoner's dilemma" argument, AKA "people will remember you being a jackass", sounds much more plausible.

comment by shminux · 2014-05-21T15:14:05.499Z · score: 2 (2 votes) · LW(p) · GW(p)

I made no argument that cooperation emerges in the PD environment, quite the opposite. I argued that, once it emerged in a non-PD environment, it does not necessarily die out in a PD environment. No group selection required.

comment by V_V · 2014-05-21T14:37:36.357Z · score: 0 (0 votes) · LW(p) · GW(p)

That's a group selection argument.

Group selection effects are significant when the individuals of the group have a very high genetic similarity, making it overlap with kin selection. Typical examples are the cells in the body of a multicellular organisms or eusocial organisms in a hive.
In groups made of mildly related individuals, like those produced by mammalian sexual reproduction (e.g. a wolf pack, a human tribe), individual selection will typically overwhelm group selection barring extreme selective pressures.

Social mammals of species which exhibit non-kin altruistic cooperation all have the ability to detect and punish defectors. One-shot PD scenarios are rare, while iterated PD scenarios are much more common in social environments, creating a selective pressure to evolve tit-for-tat strategies.

comment by Luke_A_Somers · 2014-05-21T22:32:37.121Z · score: 1 (1 votes) · LW(p) · GW(p)

Every day we deal with a thousand 'games' that are really uninteresting because the payoff matrix is so lopsided that we don't even think about it.

If we take those situations out of the denominator, what does the fraction look like?

comment by torekp · 2014-05-22T00:47:54.819Z · score: 0 (0 votes) · LW(p) · GW(p)

In the context of evolutionary psychology, taking those situations out of the denominator might be a bad idea, leading to biased thinking.

comment by Luke_A_Somers · 2014-05-22T15:40:13.668Z · score: 0 (0 votes) · LW(p) · GW(p)

How? When do you actually reason with this ratio, actually?

comment by torekp · 2014-05-22T16:40:55.264Z · score: 0 (0 votes) · LW(p) · GW(p)

The use for Rusch's ratio is"how important is it for biologists to study this particular payoff structure"? Your suggested revised ratio wouldn't be good for that.

It might be good for something else - rationality training? But that's a different subject. I suspect that, even in that context, the PD is overemphasized, and other structures relatively neglected.

comment by Luke_A_Somers · 2014-05-23T18:12:07.647Z · score: 1 (1 votes) · LW(p) · GW(p)

Is it important for biologists to study the payoff structures like 'stab yourself in the eye' or 'get into a fight you can't win'?

comment by torekp · 2014-05-23T22:00:31.010Z · score: 1 (1 votes) · LW(p) · GW(p)

It's important to be aware of the "boring" and "stupid" payoff structures, even if their solutions are obvious. Especially when the organism can't infallibly tell which game situation it's in.