Thursday, May 17, 2012

The Prisoner's Dilemma dilemma

Last week's In Our Time on BBC Radio 4 was a discussion of Game Theory.  It was an interesting discussion as far as it went, but we want to talk about the evolutionary implications here. 

The Prisoner's Dilemma (PD) is a famous game theory game:
Two prisoners are accused of a crime. If one confesses and the other does not, the one who confesses will be released immediately and the other will spend 20 years in prison. If neither confesses, each will be held only a few months. If both confess, they will each be jailed 15 years. They cannot communicate with one another. Given that neither prisoner knows whether the other has confessed, it is in the self-interest of each to confess himself. Paradoxically, when each prisoner pursues his self-interest, both end up worse off than they would have been had they acted otherwise.  (
Both confessing can be shown mathematically to be an ESS--evolutionarily stable solution.  This is 'evolutionary' in the sense that competition for resources that involves some risk, involves similar kinds of decision-making.

Red-tailed hawk; Wikipedia
Another 'game' of evolutionary interest is called Hawk and Dove (HD), which biologist John Maynard Smith brought to prominence in the 1970's in an effort to solve the problem of how cooperation evolved.  Roughly, the idea is if there is a single resource and two competitors, each can be aggressive and try to get it all, or they each can offer to share.  You balance the expected gain by trying to out-muscle your competitor, but there is also a cost if you lose.  It's been shown that a balance can be struck in which depending on the Value and the Cost amounts, some fraction of the time--that is, with some probability--you behave aggressively, and the remaining fraction of instances, you decide to share.  That is the ESS.  The fractions depend on the Value and Cost amounts, and neither party reveals this probabilistic strategy to its opponent.

Bar-shouldered dove; Wikimedia
Both PD and HD and many other similar types of games reflect situations that are very common in human society, but also very common in Nature--ecological balances, mating competitions, competition for resources, and so on.

Game theory is immensely popular among evolutionary biologists (and others who are obsessed by the view that life is mainly about Darwinian winner-take-all competition, or who simply want to understand the balance between competition and cooperation).  There is the additional appeal that game theory usually requires sexy, sophisticated mathematics to find the right strategies, or stable ones.

If people or birds are seen to be following some strategy when they compete, it is then assumed that they probably evolved to do this.  This then whets the prurient appetites of those who want to peer into your genome to see how, despite silly illusions of free will, you're really just a genetic automaton.

So, is it realistic to assume that something so open-ended and complex as a game theory behavior could have evolved?   After all, games like PD or HD seem widespread and if birds, ants, or even humans are just complex gene machines, mustn't it be possible to pre-program them (i.e., genetically) to play the game the evolutionarily optimized way?

This is really a dilemma, because even just one game, say HD, can arise in all sorts of ways even within a given individual's lifetime.  How can genes be pre-wired to recognize all the situations and identify their similarity and then push the Play button?  After all, every brain is wired in zillions of different ways in detail.  So what kind of gene or genes could possibly produce this behavior?  Remember that genes code for proteins, and have to be regulated in specific contexts; they are not individual computer programs.

One way to answer this is by a kind of meta-evolutionary view: we may not be able to identify the wiring diagram, but the net result of evolution is a brain that can perceive the environment and evaluate costs and strategies, and figure out for itself what is best.  The selection pressure is general, and it's for evaluating conditions rather than 'for' some specific strategy.  No need whatever for any specific genes 'for' HD or PD playing!

In this view, and especially if games really are cosmically mathematical (as they must be, given how widely they are found and shown to have similar strategy properties), then a brain that is somehow good at evaluating the real world will figure this out and identify the better strategy.  The same brain is faced with multiple and diverse evaluation situations, so that all we need is overall evaluative ability to get what we see, however such ability actually can be built into neural synapses and the like.

One would certainly easily be able to relate this to probabilistic strategies like HD, because each individual is more or less guessing what to do each time, the result being an empirical probability--the observed fraction that individuals act like hawks, or doves.  Likewise, one could observe that played something like PD properly, because s/he figures out the general risk-benefit situation.  No need for specific evolution of some convoluted gene-based mechanism specific to the game (which would imply the same to evolve separately at the gene level, for every other situation-evaluating things that animals do).

This is a way in which things can be 'genetic' in a general sense, but not specifically hard-wired by selection for a specific task.  That's a big difference!

It is genetically deterministic in a sense, by not in the precise Darwinian sense so often invoked, explicitly or just under the surface, so routinely in discussions of behavioral evolution.


Holly Dunsworth said...

This is nice.

I'd like to add that a problem I have with so many behavioral strategy discussions is they lack much acknowledgement of learning and environment- that an animal can be biased toward engaging in some behaviors more than others (or at all) simply because it's what others around him do.

Ken Weiss said...

Right. And for many species, certainly mobile ones like us, being able to learn from unpredictable environments and situations would seem an obvious way to be 'adapted'.

It is easier to think of a 'gene' (or some fixed set of genes) 'for' playing Prisoner's Dilemma, and a separate set for other games, than to try to imagine how all our genes could evolve to make us environment-assessors/responders. But selection working on the net result seems to have done it.

It's just not as satisfying since it doesn't lead to a specific gene to study. Not so neat a story!

Well, is that so? Isn't it just as neat, or even neater, that what matters is the phenotype, and learning ability is an incredibly fascinating phenotype, and one doesn't have to think about genes at all to marvel at it, and want to understand it.

Just as we don't need to study each stone to admire the Taj Mahal.

Anne Buchanan said...

Wonderful example of the Prisoner's Dilemma in action. Game show head games.

rich lawler said...

Alan Grafen made a similar point to yours and called it the phenotypic gambit: model the evolutionary basis for a behavior as if the simplest genetic system controlled it.

More generally, game-theory, like kin selection, just relies on "behaving." You just behave in a particular fashion and to the extent that the behavior is beneficial (and heritable) then your behavior might be picked up by selection. No need to make complex calculations of strategies (or relatedness) in your brain.

What game theory doesn't yet incorporate well is drift. Once the strategies are set, the "game" is entirely deterministic. Getting a particular strategy off the ground is likely going to be more due to drift than selection. Game theory assumes an immediate population response by a superior strategy, but in the real world, it's not clear that the population can respond so quickly (due to drift and demographic stochasticity).

Ken Weiss said...

If I understand your second paragraph, the question is whether the fitness advantage is because the brain is specifically tailored to do the particular game, or just tailored to evaluate the realities of its environment and figure their implications out.

Unless there is evidence to the contrary that I'm unaware of (certainly a possibility), the specific behavior itself need not be heritable.

For example, there need not be a specific gene or genotype 'for' understanding the nature and ubiquity of gravity. If you drop something, it falls, and if the brain can learn that, it need not be pre-wired for it. And there need not be a separate genotype to learn when something rests on or partly on something else and hence won't fall down.

Someone too dense to learn these things about its environment, would get eaten by a predator or something, and be selected against, and for whatever brain-related genotypic reason might be involved, those variants would go.

A programmable computer is a lot more versatile and hence advantageous than one like, say a digital watch, that can only do a few pre-specified things. (and here I'm not speaking of Payley's Watchmaker!)

If we had to evolve task-specific genotypes, we'd need genes for chess and contract bridge. This goes back, in a sense, to Alfred Wallace's argument (which was Paley-like) that our ability to do calculus couldn't have evolved because our ancestors didn't do calculus, so must have been put in our brains by God.

rich lawler said...

I think we are probably more in agreement than not.

I'm saying the following. In the Hawk-Mouse game (the original animals used by Maynard Smith and Price), or any other frequency-dependent situation, the animal doesn't make any "complex" calculations in its head (but see below). The pay-off is immediate. So envision that there are four behavioral options, two or three of which correspond to options in the Hawk-Mouse game. If they animal randomly engages in one option, which is the correct "move" given its opponent's "move" then it will gain the payoff. The animal just "behaves" and natural selection provides the payoff.

If the animal has a simple form of memory (which need not be heritable, as you point out), it can begin to develop what we might call strategies when the games are repeated. A simple one is known as "Pavlov"--do what you did last time if you won, otherwise shift your strategy. Others, as you know, are "tit for tat"--cooperate first, then do what your opponent did last time, and another is "always defect"--never cooperate, a strategy that is an ESS in the prisoner's dilemma.

I guess the key thing here is the idea of memory with respect to the different "moves" one can make when the PD or other games are repeated. Pavlov requires you to remember two things, what you did last time and if you won. Tit for Tat requires you to remember only what your opponent did last time. These strategies are quite robust to all other strategies played against them, and it seems that many animals, even insects, could engage in them.

If the strategies (or just memory) are heritable, then you can get lineages of animals playing different strategies. Environmental unpredictability is certainly a challenge for game-theory but as I noted, game theory was never designed to deal with unpredictability since the game is deterministic once the strategy sets are determined. The only way around this is to assume a new ESS will invade the population quite rapidly if the environment changes.

To me, game theory was a simple way to model the complexities of frequency-dependent selection independent of cognition, braininess, or the subtle machinations of the human mind. There are usually a very limited set of moves and with minimal assumptions (some form of memory, either hard-wired or flexible), you can get animals interacting in seemingly complex ways. The fact that it is often applied to humans only shows that humans often behave as if we are "controlled" by simple genetic-based algorithms when everyone knows that we are not.

Ken Weiss said...

Yes, we basically agree.

Tutu said...

The diagram is wrong, it's reversed.