Prof: Okay,

this is the second lecture on behavior.

And today what I want to do is

I want to give you one of the major analytical tools for

dealing with behavior, which is evolutionary game

theory. And before I get into the body

of the lecture, basically I want to tell you at

the beginning of the lecture where it came from–

it came out of Economics–and I want to tell you that I’m going

to give you two examples of particular games;

one is the hawk-dove game, the other is the prisoner’s

dilemma. And it turns out that neither

of these games is really directly testable with good

biological behavioral examples. So instead of actually testing

these ideas with biology, what I’m going to show you is

how biology introduces interesting qualifications to

the assumptions of the games. And so I’ll give you the two

games, and then I’ll give you a series

of biological examples, and then comment on how that

really changes our thinking about the assumptions of the

games. But before I go into all of

that, I want to signal– and I’ll come back to this in

the last slide– that evolutionary game theory

is one of the parts of evolutionary biology and

behavior that connects this field to economics and political

science, and that the prisoner’s dilemma

model, which I will present in the

middle of it, actually is a particular

embodiment of the tragedy of the commons,

which is, of course, affecting the way that we use

all of our natural resources, and methods for solving the

tragedy of the commons are actually central issues in both

economics and in political science.

So this is actually an area in

which there are strong trans-disciplinary connections

of ideas. So the basic idea behind an

evolutionary game is that what you do depends on what everybody

else is doing, and that means it’s going to be

frequency dependent. In other words,

if I decide to be aggressive, in a certain environment,

the success of that will depend upon the frequency with which I

encounter resistance. So game theory is fundamentally

frequency dependent. And the central idea in

evolutionary game theory is that of the evolutionary stable

strategy. So I’m going to show you that

that, in fact, is equivalent to a Nash

equilibrium. So when you’re playing a game

against another member of a population it’s not like playing

a game against the abiotic environment,

because your opponents can evolve.

It’s not like you’re playing a

game against, you know, in a sense of staying

in the game against winter temperatures,

or something like that. You actually have an opponent

that has a strategy, and the strategy can change.

So that makes the whole

analysis of games the analysis of a move and a counter-move,

and that counter-move can either be dyadic,

where you’re playing against one other player,

or it could be that you could conceive of it as playing

against the entire population. So there are some nuances there.

And in that sense evolutionary

game theory is really very fundamentally co-evolutionary;

it’s always about how your strategy co-evolves with the

other strategies that might pop up in the population.

Okay?

But it’s strategies within a

population. Co-evolutionary game theory is

really not applied so much to one species evolving against

another. It’s usually,

how will my behavior do against the other behaviors that are

present in the population? Okay, where did it come from?

Well here are some of–here’s a

little gallery of heroes. Basically it comes out of von

Neumann and Morgenstern’s book on game theory,

which was published I think in 1944,

as then further developed by people like John Nash and

Reinhardt Selten. So these guys more or less

founded it. And you can actually go into

Maynard Smith’s book on evolutionary game theory and

pull out of the appendix of von Neumann and Morgenstern one of

the payoff matrices that they use;

I mean, you can see that these guys were actually studying that

book, and then developing it in an evolutionary context.

John von Neumann was a

Hungarian genius who managed to show how some of the basic

problems in quantum mechanics could be connected and

explained; he did that back in 1929,

and then he went on more or less to invent the idea of an

operating system for computers. So he contributed very greatly

to the conceptual underpinnings of the information revolution;

and he also invented game theory.

So John von Neumann was a

bright guy. John Nash, of course,

is famous from the book and the movie A Beautiful Mind,

as the fellow who saw at Princeton that the stable

solution to a game that is being played between two parties is

that the stable solution is the one that you play when everybody

else is playing their best possible strategy.

Okay?

That’s the insight that he had

in the bar at Princeton, as a graduate student,

and then he succumbed to his schizophrenia and didn’t really

recover until he was in his sixties.

And Reinhardt Selten is a

German professor who developed game theory in the context of

economics, and generalized it into all

sorts- using all sorts of alternative assumptions.

And these two guys shared the

Nobel Prize in Economics for it. So that’s where it came from.

And these are some of the key

events that I’ve just gone over. And then these ideas were

developed by George Price, a really remarkable guy,

and John Maynard Smith, and applied in biological

behavior. And John’s book came out in

1982. So it had a lot of impact.

And if John had just been

willing to recognize and acknowledge that in fact an ESS

is a Nash equilibrium, he probably would’ve shared in

that Nobel Prize. But he didn’t.

This is John.

He was a very good dishwasher.

I spent a lot of time with him.

So that’s one of my photos.

And really the key figure that

stimulated John, just as he stimulated Bill

Hamilton, was George Price. And George Price was developing

these ideas in the context of the puzzle of altruism and

cooperation; how did cooperation and

altruism ever come to be in an evolutionary context?

And you’ll see that when we

come to the prisoner’s dilemma and I talk about Axelrod’s

experiment with competing different strategies against

each other on a computer, that Price really actually

contributed twice to the solution,

or to our thinking, about this problem of where did

altruism and cooperation come from?

One, in the context of game

theory, and once in the context of kin selection and

hierarchical selection. Okay, here are the basics.

The basic thing that you ask in

game theory is can any conceivable alternative invade?

And this turns out to be

why–by invade I mean will a mutation come up that modifies

behavior, and if it comes up, will it increase in the

population? If it’s going to increase in

the population, it will do so because it has

greater lifetime reproductive success.

So if that gene affects a

behavioral strategy in such a way that over the course of the

lifetime it increases the reproductive success relative to

other strategies, that will be what we call

invasion. So if alternatives cannot

invade, then that means that the resident strategy,

the one that’s already there, is an evolutionary stable

strategy. So the stability means

stability against invasion; stability against alternatives.

Now you might ask yourself,

how do we know what all the alternatives are?

And the answer is in reality we

don’t. But in theory we can imagine,

if we restrict our attention to a certain scope of possible

behaviors, that the alternatives are all

the possible combinations of behaviors within that restricted

set. Okay?

So that is actually the thing

that’s going on. The theorist is sitting there

and saying, “Should I be more aggressive or less

aggressive?” Well all the possible behaviors

consist of not being aggressive at all, or being very

aggressive, and everything in between.

So those would be the ones that

you tested against. You’ll see how that works when

we go through a couple of examples.

So the ESS is then a strategy

that resists invasion, and it turns out that it’s

exactly the same thing as a Nash equilibrium.

So when John Nash solved this

problem for game theory, back in Princeton in I think

1951, he in fact was also at the same time solving the problem

that Maynard Smith and George Price posed in I think 1973;

just in a different context. So here’s a simple game,

and this is one of the first that Price and Maynard Smith

cooked up, to try to illustrate how you

would apply this thinking to animal behavior.

And they called it the

hawk-dove game. So two animals come together,

and they’re going to fight over a resource,

and that resource has value V, and that means that the fitness

of the winner will be increased by V.

Okay?

The loser doesn’t have to have

zero fitness, it’s just what–it’s the

increment in fitness which is determined by this particular

encounter that we’re talking about.

So we say, “Well,

they can have one of two strategies;

they can be hawks or doves.”

And the idea is that the hawk

strategy is that you escalate and you continue to fight either

until you’re injured, in which case you have to back

off because you can’t fight anymore,

or until you win and the opponent retreats,

in which case you get the whole thing.

And the dove strategy is that

you go up and you display, and if the opponent escalates,

you back off immediately and run away,

and if the opponent doesn’t escalate you’ll see that you’ll

share the resource. Okay?

If two hawks encounter each

other, then one or both are going to be injured,

and the injury will reduce fitness by a certain cost.

So being a hawk has a benefit

in that you can be aggressive and acquire resources,

but it has a cost in that if you run into another hawk,

you can get beaten up and injured.

So this is sort of the

fundamental intellectual construct of game theory;

it’s a payoff matrix. And the idea is that it lays

out, for the things on the left, what happens to them when they

interact with the things on the right.

Okay?

So when a hawk interacts with a

hawk, this is its payoff. When it interacts with a dove,

this is its payoff. When a dove interacts with a

hawk, this is its payoff, and when it interacts with a

dove, that’s its payoff. I’m going to take you through

that. So if a hawk encounters a hawk,

it has a fifty percent chance of winning and a fifty percent

chance of being injured. So its payoff is one-half of

the benefit minus the cost. So you just see we’re kind of

averaging that payoff over many such possible encounters.

So the assumption here is that

hawks are total blockheads and they escalate blindly;

they disregard differences in size and condition;

they’re really stupid, they just go in there and they

fight for the resource, and they don’t have any nuance

to them at all. The dove will give up the

resource. If a hawk encounters a dove,

it gets the resource, the dove gets zero.

So it gives it up and the hawk

gets it; and that’s what these entries

in the matrix mean. Okay?

So the hawk is encountering the

dove, the dove is encountering the hawk, the hawk gets V,

the dove gets zero. That doesn’t mean it has zero

fitness, it just means that its fitness doesn’t change because

of the encounter. It doesn’t get anything in

addition, but it also doesn’t lose anything.

So you can think of the dove as

a risk-averse strategy. When a dove meets a dove,

they share it. They sort of shake hands and

say, “Hey, 50/50.”

Now if a strategy is going to

be stable, then it must be the case that

if almost all members of the population adopt it,

then the fitness of the typical member is greater than that of

any possible mutant; otherwise a mutant could

invade, and that would mean the strategy wasn’t stable.

So in this case if we let W of

H be the fitness of the hawk, and W of D be the fitness of

the dove, and E of H,D be the payoff to

an individual adopting a hawk against a dove–

and we have two possible strategies,

I and J; so these are going to be,

in general, what we’ve instanced by hawk

and dove here– I is going to be stable if the

fitness of I is greater than the fitness of J.

And if the mutant J is at very

low- when we assume the mutant is at very low frequency.

So if I is going to be stable,

at very low frequency, then when I encounters I,

it has a higher fitness than when J encounters I.

Or when I encounters I,

it has the same fitness as when J encounters I.

And when I encounters J,

it has a greater fitness than when J encounters J.

Okay?

So this is just a way of being

very careful and logical about laying out the different

possible relationships of fitness on encounters.

Now what happens?

Well dove is not an ESS.

If a population is 100% doves

and one hawk pops up, it’s going to interact almost

all with doves. It’s not going to run into any

hawks. It’s just going to go around

beating up doves and taking away the spoils.

So it will invade.

Hawk will be an ESS if the

payoff of an encounter is greater than the cost of the

encounter. Okay?

Now even if the population is

100% hawks, and every other individual it

encountered is somebody that fights and beats you up,

that will be stable if V is greater than C.

But what happens if V is less

than C? Well if the cost of injury is

high, relative to the reward of victory, then we expect mixed

strategies. That means the following:

if we–well I’ll ask you to play this.

Just think about this situation

a little bit, and I would like you to take

just a moment to explain what’s going on to each other,

and then I’ll ask one of you to tell me what happens when you

start with 100% doves and a hawk mutant pops up,

and another of you to tell me what happens when you have 100%

hawks and a dove mutant pops up, when this condition is the

case–okay?– when it really hurts a hawk to

encounter another hawk? So take a minute to describe to

your partner what that frequency dependence is like,

and then I will ask one of you to replay each of those cases.

Okay?

>>

Prof: Okay, let’s go.

Who would like to explain what

happens when you have a population which is 100% hawks

and a dove crops up as a mutation?

What happens?

Student: Mutation by the

hawk doesn’t, because the doves are able to

>. Prof: Okay.

Why did that happen?

Student: Because every

time it repeats it, every time

>, and there’s never a situation

where>. Prof: Well actually it

doesn’t happen Manny; it’s not quite like that.

Remember what the payoff is for

the dove. When the dove encounters a

hawk, its payoff- its fitness doesn’t alter.

Okay?

Another idea.

Student: It will

increase in its cost because since there’s a dove reaching

out at the hawk as a dove, it gains I guess a lot more

than it gains just because of the hawk.

And you said the fitness of the

dove wouldn’t change. So that one dove will at least

be present. So it will

>. Prof: Yes,

what’s the average fitness of the hawks in that population?

Student: One-half V

minus C. Prof: Yes,

and V is less than C? Student: Yes.

Prof: So it’s a negative

isn’t it? Is 0 bigger than a negative

number? What happens to the doves?

They increase.

They increase because they

actually don’t bear any cost at all when they run into a hawk;

their fitness is not decreased. And so basically they are a

neutral allele that’s introduced into the population,

and if they have perfect heredity, they start

reproducing. Right?

And basically what’s going on

is that the hawks are mutilating each other.

They’re damaging each other so

much that even though the dove’s fitness is zero on this scale,

it’s still greater than the hawk’s,

which when the hawks are mostly encountering hawks is negative,

on this scale. Okay, now let’s turn it around.

What happens when it’s all

doves and a hawk enters the population;

what happens? We have a population that we’ve

just made in our mind. It’s 100% doves and a hawk

comes in. Student: It really

depends if it’s a hawk. Prof: Go further.

Student: So if there’s

one hawk,>.

Prof: Yeah,

it goes like gangbusters. It only meets doves;

it never gets beaten up by another hawk.

Student: So if there’s

>. Prof: Yes,

and so it just keeps going. Right.

So from either side,

from either 100% doves or from 100% hawks, the vector is

towards the middle somewhere; and where it’s going to

stabilize depends on the relationship of V and C.

Okay?

That’s why this is a mixed

strategy. Neither strategy is an

evolutionarily stable strategy. The only reason that they can

persist, with this relationship of V to C, is that they come to

some kind of intermediate frequency.

If there’s too many hawks the

doves will win out, and if there are too many doves

the hawks will win out. Okay now, so that’s one- that’s

an example of a game that will result in a mixed strategy.

Now let’s look at the

prisoner’s dilemma. Okay?

So this is the payoff matrix

for player one, this is the strategy of player

one, and this is the strategy of player two.

And C stands for cooperate and

D stands for defect. So basically the reason this

game is set up this way is that it’s trying to show you that it

would be better for both players to cooperate,

but both players are actually motivated to defect,

and so if you have short-term selfishness,

which is determining the outcome, defection will win over

cooperation. So that you will not,

in this circumstance, just playing this game one

shot, you will not get the evolution of cooperation and

altruism out of the prisoner’s dilemma.

Instead you will get the

tragedy of the commons. So the entries here.

This is the expected value of

cooperator playing cooperator; cooperator playing defector;

defector playing cooperator; and defector playing defector.

And if we put in some

particular numbers that actually represent an instance of the

general conditions, these particular numbers are

chosen in such a way that defection will in fact be

selected. So cooperation will be an ESS

if the expected value of C playing C is greater than the

expected value of D playing C. Okay?

And that’s not the case.

D will be an ESS if the

expected value of D playing D is greater than the expected value

of C playing D; which is true.

Now look at the payoffs:

3 is greater than 1. If the population were all

cooperators, everybody would get 3.

If the population is all

defectors, everybody only gets 1.

But because of the way the

payoff matrix is set up, with the interactions between

the cooperators and the defectors,

this is the evolutionary stable strategy,

and this one, which is great for the group,

is not stable against invasions by defectors,

because the payoff to a defector, who is playing against

a cooperator, is even greater.

But when a defector plays

against a defector, life gets pretty unpleasant.

So in fact this is the tragedy

of the commons. So the general condition for

this, okay, if we do the algebra

rather than the arithmetic, is that the stable strategy is

always to defect from the social contract,

always not to cooperate, if T is greater than (*>*) R,

R *>* P, P *>* S, and R *>* than the average of S

and T. So that this all has been

analyzed in detail, and this is sort of the

paradigmatic social science game that is used in many contexts.

Now what if you play it again

and again? This was the first idea about

how even in this circumstance, even if you’re playing a

prisoner’s dilemma game, with rewards set up like this,

you could get the evolution of cooperation.

Just do it again and again.

Okay?

So you’re not just playing

once, you’re playing many times against the same person.

And a very simple strategy

turned out to work. Bill Axelrod,

at the University of Michigan– he’s a political

scientist–said, “I want to hold a computer

tournament, and I want everybody around the

world who’s interested in this issue to send me their computer

program to play against other computer programs,

in an iterated prisoner’s dilemma.”

And it turned out that a very

simple one did extremely well, and that is Tit-for-Tat.

So you cooperate on the first

move–if you’ve run into a defector, you get beat up by

him; if you run into a cooperator

you win, both of you win. And then you do whatever the

guy did last time. So the essential features of

Tit-for-Tat, that make it work, is that it retaliates but it’s

forgiving, it doesn’t hold a grudge.

Okay?

The other guy defects on you,

you’re going to punish him. If he switches to cooperation,

you say, “Oh fine, I don’t hold a grudge,

I’ll cooperate with you on the next time.”

So after a huge amount of

research, it turns out that there are

some extremely nuanced and complicated strategies that can

do a little bit better than Tit-for-Tat.

But the appeal of Tit-for-Tat

is its simplicity. It doesn’t take very much

cognitive power to implement this behavioral strategy.

It doesn’t take very much

memory to implement it. Okay?

It seems to be something which

is simple and robust and that wins.

Now as soon as you put in

space, you can get a much more complex strategy.

And the take-home from that is

that if you have what’s called population viscosity,

which means that particular individuals tend to encounter

each other more spatially than if they’re just randomly mixed

up in the population, that promotes cooperation.

So Martin Novak,

up at Harvard–actually he was at Princeton when he did this–

he came up with a whole lot of nice,

two-dimensional representations of those games.

And this is one possible

outcome here. Okay?

So here blue is a

cooperator–and these guys are, by the way, playing prisoner’s

dilemma, and they’re playing prisoner’s

dilemma against their neighbors; they’re not playing randomly in

space, they’re actually playing against the neighbors that are

physically sitting right there. So blue represents somebody

that was a cooperator on the previous round and is a

cooperator now; whether they retain in the

population or not depends on whether they’re losing or

winning in the encounters. Green is a cooperator that was

a defector. And here you can see that here

are some cooperators that have won against some defectors,

and they’re forming a little ring right around that little

blue island of cooperation. And red is a defector that was

a defector, and yellow is a defector that was a cooperator.

And what happens in this

particular game is that the percent cooperation goes up,

comes down, stabilizes right at 30%.

So in a situation in which–the

prisoner’s dilemma suggests, if you just consider an

interaction in isolation, it’s going to be 100%

defectors. Just putting in space and

giving individuals a chance to interact repeatedly with other

individuals creates a situation where often cooperators are

actually interacting with cooperators,

and they’re getting a win, and as soon as they build up a

little spatial island of cooperation,

they do great. So they hold their own in a sea

of defectors, just due to the two-dimensional

nature of the interaction. Okay, so thus far in the

lecture I have give you pretty abstract mathematical kinds of

stuff. And what I now want to do is go

into a series of biological examples.

And the biological examples are

not direct tests of evolutionary game theory.

What they are is the

application of game theoretical thinking to biological contexts,

that then inform us about the assumptions that we’re making in

the games. And one of the early

applications was to the bowl-and-doily spider.

So this is a female

bowl-and-doily spider. It doesn’t really show her bowl

and her doily, but basically what she does is

she spins a web that looks like a bowl,

and then it has a layer down below it that looks like a

doily, and she puts up trip lines that

go up above it, so that insects that are flying

along hit one of these trip lines and fall into the bowl,

and she’s sitting on the doily and she comes up and grabs it.

Okay?

And it’s on the doily that the

mating interactions take place. So this figure should look

pretty familiar to you from the last lecture.

Insemination in spiders works

pretty much like insemination in dung flies.

The probability that a male

will fertilize eggs increases from the start of copulation up

to a certain point, where he’s getting perhaps 90

or 95% of them. So he’s getting diminishing

marginal returns as he sits on the female.

And in this study the contrast

was between a resident male who actually had gone in and had

successfully displayed to the female,

and knew whether or not copulation was actually now

taking place, or was going to take place,

and a new intruder who’s coming in.

So if the resident is somebody

who’s going to have this experience,

and the intruder coming in has no idea what’s been going on–

okay?–we will assume that the intruder knows nothing about the

shape of this curve; it may know that the curve has

started but it knows nothing about the shape.

So it has to simply make an

assumption about the average value of that female–the

intruder is a male. Whereas the resident knows what

this curve is, then the payoff to the resident

gets greater and greater, the longer the copulation goes

on, and then it drops towards the end of the copulation.

It’s already gotten 90% of the

eggs. Okay?

And so actually this happens

pretty quickly, which is kind of nice;

I mean, if you’re doing a behavioral study in the field,

it’s nice to have it over quickly so you can get your data

quickly. Only seven minutes after the

beginning of insemination that female doesn’t have very much

more added value to that male and he would be better going

off– as you know from the marginal

value theorem, that line, at the tangent,

is going to be crossing probably somewhere up in here–

it’s good for him to jump off, try to go find another female.

Whereas that intruder coming

in, not having so much information about the system,

at least on a simple assumption, just thinks,

oh, the female has a certain kind of average value,

and I’m not- I haven’t been able to copulate with her yet,

so this is what I expect. Okay?

Well if you look at the actual

behavior of spiders. This is the observed,

this is the predicted. So the predicted is that the

percentage of fights that would be won by the resident would go

up; he would fight really hard if

he were interrupted, after a certain point in

copulation, assuming he could start over

again, and that after he had been

copulating for seven minutes, he wouldn’t care anymore.

So the prediction is intensity

of fighting would peak and then drop;

and the observed values seem to follow that pretty well.

So here’s the twist on game

theory. The cost-benefit ratio in the

payoff matrix is being altered by the behavior of copulation,

and one of the participants knows and the other one doesn’t.

So the thing that this example

introduces into evolutionary game theory is the whole issue

of who has information on the potential payoffs of the game,

and it shows that that makes a big difference.

Okay?

And that’s not in the

assumptions of hawk versus dove; it’s not in the assumptions of

the prisoner’s dilemma. This is some important aspect

of biology that alters that analysis.

So this just runs through what

happens. You put both males in at the

start, the bigger male will win. Okay?

So if neither of them has any

information, any more information than the other,

the big one wins. If they’re the same size,

the fights are settled by what’s the difference in reward?

Okay?

So the resident will fight

longer and will be more likely to win at the end of the

pre-insemination phase, but intruders are more likely

to win after seven minutes of insemination.

If a resident is smaller than

the intruder, they persist longer,

when the reward was greater. So you will find weenie little

runts fighting great big bullies if they know something about the

reward they’re going to get. And if the costs and benefits

are nearly identical, they’ll fight until one or both

are seriously injured or in fact dead.

So this is another way,

of course, of underlining that the payoff in evolution is

number of offspring, not personal survival.

So they’re willing to risk a

lot, if there’s a lot on the line.

So that’s one biological

example, and that’s the bowl-and-doily spider.

This next example has to do

with Harris sparrows. And again it has to do with

information, but now it also has something to do with honest

signaling and perception. So there is a sense here in

which what you’re going to see is simple-minded sparrows

getting really ticked off at being deceived.

Okay?

So this is a study done by

Seivert Rohwer, who’s in the museum at the

University of Washington in Seattle,

and what he noticed was that if you just go out in Nature,

you see a lot of variation in how dark the heads of the males

are, and that these guys with the

dark heads are dominant and they win most of the fights.

And by the way,

you see a lot of this in birds, that they have a signal that

they can give that is a signal of their condition and of the

likelihood that they might be able to win a fight if they got

into it. So here are some of the

experiments; and so I put up Appearance and

Reality. Okay?

I don’t know if Harris’s

sparrows analyze the problem philosophically in terms of

appearance and reality, but they certainly react to

appearance and reality. So what Seivert did was he

experimentally treated subordinates,

either by painting them black, or by injecting testosterone,

or by painting them black and injecting them with

testosterone. So if you paint them black,

they look dominant; they behave- they do not behave

dominant because they don’t know they’ve been painted black,

and they don’t have the testosterone in their system.

Okay?

Do they rise in status?

No.

If you inject them with

testosterone, they behave like they’re

dominant, but they don’t have the signal that they’re dominant

and they get beaten up, they do not rise in status.

Because basically what they’re

doing is they’re behaving in a very–according to bird

lore–they’re behaving in a very deceptive fashion.

But if you do both things,

you paint them black and you inject them with testosterone,

then you do to them essentially what evolution and their

development has already done to them,

which is that the black is actually naturally expressed in

male individuals that have higher testosterone levels:

they look dominant, they behave dominant and they

rise in status. So this is a very interesting

observation right here. Okay?

Now that’s one twist on

evolutionary game theory. It says that your perception of

your opponent, and your understanding of

whether he’s trying to deceive you or not, is an important

thing. However, there is another

issue, and that is that it always pays to assess before

escalating. When I was in grad school we

had a Great Pyrenees, a great big dog,

Aikane. His head stood about this high;

he weighed about 130 pounds. And we were living in a suburb

of Vancouver, British Columbia.

And I was out for a walk one

day with Aikane, and a great big aggressive male

German Shepherd came around the corner,

about fifty feet away, and each dog went on alert,

ears went up, hair went up on the back.

They started barker ferociously

at each other. They rushed,

at high speed, at each other.

I was thinking,

“Oh my God, I’m going to have to pull a

fight apart.” They went by each other,

like ships in the night, went about fifty feet down the

road, and they both urinated on a post and trotted proudly away.

They had managed to avoid

serious damage. Well that’s what’s going on

with Red Deer. If Red Deer get into a fight

where they are really about equally matched,

they can end up locking antlers in such a way that they can’t

extricate themselves and they will actually starve to death.

Also, if they are swinging

those nice pointed antlers around in a fight,

they can rip out the eye of an opponent,

they can get a wound that will be infected,

and they’ll get bacterial sepsis and die from an

infection. So fights are dangerous.

But fights are the only way

they can get babies. So what they do is they first

do a lot of assessing. They approach each other and

they first roar. So if you’re around moose in

the fall, or deer in the fall, you will hear roaring,

and that’s what they’re doing. Basically the ability of a male

deer to make sound is pretty directly proportional to how

good- what kind of shape he’s in.

So if that sound is equally

impressive, then they get into a thing where they do a parallel

walk; they actually walk next to each

other, kind of sizing each other up.

And it turns out that if

they’re very closely matched in size, these parallel walks can

go on for four or five hours. They’ll just be wandering all

over the landscape, trying to see who’s going to

give up first. Okay?

So that’s the parallel walk.

And in a certain number of

cases one stag will say finally, “Well, looks like I’m

going to lose this one, it’s not worth fighting.”

And then finally after doing

that parallel walk thing, if it’s not resolved by then,

they will fight, and one will win and one will

withdraw. So the point of this is that

actual fights among animals are much more nuanced than the

simple Hawk-Dove game would ever have you believe.

And I think it’s probably true,

throughout all sorts of tradeoffs in evolutionary

biology, that every time there is a

significant cost, there will be some modification

of behavior, or some way of tweaking that

cost, that will arise, that will reduce the cost.

So this is all cost reduction.

Okay?

They need to get their mating,

but they’re going to do it in a way that’s not going to kill

them, if at all possible. And that’s not in the simple

assumptions of any of the evolutionary games that I showed

you. So how solid are the

assumptions of this whole way of looking at the world?

Well it turns out that the

assumption is being made is that you’ve got a big randomly mixed

population. If you put in kin selection,

so that the opponents can be related to each other,

so that a brother might be fighting with a brother,

the analysis gets complicated, but the result’s simple:

if you’re related to the other player you’re nicer.

That’s not surprising.

If you have repeated contests

and there’s an opportunity to learn, the results will change.

Okay?

If there’s no learning,

then having the series of contests really doesn’t make any

difference. So it is the ability to learn

and to remember that turns the repeated prisoner’s dilemma into

a situation in which cooperation can evolve.

So you have to have some

cognitive capacity to do that. If the population is very

small, mutants might not be rare, and the basic model has to

be altered. It turns out that asexual

reproduction doesn’t matter too much.

The sexual system–we usually

get to the ESS if the genetic system will produce it;

you know, will allow it–is you have more genes affecting a

trait, it becomes more likely that the population will hit the

ESS. If you have asymmetry in the

contest, that will–as we’ve seen with

the bowl-and-doily spider, and with the size of the

contest, size of body size, and with badge size in sparrows

and in deer– that will change the outcome.

If you analyze pair-wise

contest versus playing against the whole population,

it turns out in general a mutant really is playing against

the whole population. There you actually have to do

it on a computer usually; you can’t–it’s hard to analyze

analytically. But it doesn’t make a huge

difference. Okay?

So the take-home points that I

want you to get from evolutionary game theory is that

this is a tool, it’s an abstract tool,

and it is probably the tool of choice anytime you’re looking at

frequency dependent evolution of phenotypes.

It is very often good for your

mental health, as an evolutionary biologist or

behaviorist, to test some property against

the invasion of all possible mutants.

That’s a very useful criterion.

So, for example,

if you are thinking about those red grouse in Scotland who are

out in the fall in a big assembly,

and somebody says, “Oh, the reason that they do that is

so that next spring they won’t reproduce so much.”

And you ask yourself,

“What if a mutant crops up in that population that doesn’t

think like that and it’s just going to reproduce like

gangbusters, no matter how dense the

population is?” That little thought process

tells you the explanation that was being given doesn’t work,

because that selfish mutant will invade.

Okay?

So it’s a very useful criterion.

And I’d like to recommend Ben

Polak’s course. Ben is a very good teacher.

Ben’s gotten teaching awards.

He teaches an Econ course on

game theory, and it will lead you through this stuff.

And Ben is very good at

actually having you do homework assignments in which you solve

games; which is more than this course

has time for. So if you want to get your head

around this, I recommend Ben’s course.

And next time we’re going to do

mating systems and parental care.

Welcome to our blog!