Hello, welcome to mooc lectures on Strategy,
An Introduction to Game Theory
In this module, I am going to introduce a new concept
evolutionary game theory.
Before, we begin with evolutionary game theory,
we should understand basic of evolutionary biology.
What is the basic of evolutionary biology?
The idea there is very simple, that genes
the genetic code present in all the animals
are the prime determinants of their observable
characteristics, this observable characteristics
is called fitness.
So, what do we say, more fit organisms on
average, typically they have better reproductive
success, it means they produce more offspring
they produce more kits.
Meaning, that the genes which provide greater
fitness get increase representation in the population.
So, a particular gene, let us say that a particular
gene represents a particular characteristics
in the animal and if it is, it has greaterfitness this will spread in the whole population of that animal.
And, the fundamental of evolutionary biology
is that the notion of natural selection as
the mood of evolution.
So, what we have now, we have only be discussed
for four weeks regular game theory, now we
are calling it regular game theory in the
sense as suppose to evolutionary game theory.
What happens in the regular game theory?
We have players and the players are rational,
they rationally they make decision.
Not only they make decision rationally, but
they make those decision consciously and also
the important thing is that they strategically
they make decision.
So, there are three factors players, who make
decisions rationally, consciously and strategically.
As oppose to regular game theory, if we look
at the evolutionary game theory, because it
concerns with the evolution, what happens
the players there and animals would be the
players, animals a particular animal would
not consciously or rationally or strategically
would be making any decision.
But, what we say that game theoretic concepts
would continue to apply, even if no player
is using any reasoning or making conscious
decision.
Of course, they are the vehicle, if as things
are happening in a particular manner, because
players are interacting a strategically rational
players are interacting rationally.
Here, what is happening, that the behavior
is encoded in as a gene.
And, if a behavior leads to better outcome,
then that gene would have better success in
spreading in the whole population, so that
is the key.
Fundamental question in the regular game theory
is, that how does strategic interaction among
the players decide the outcome of a game.
Here, the fundamental question in evolutionary
game theory would be which behavior will persist
in a population.
If, a particular behavior leads to better
fitness, notice the gene gets represented
by behavior, can lead to better fitness, better
fitness means better reproductive success.
So, if gene is having better productive success,
then it will get the spread out in the population.
Here, natural selection replaces the rational
behavior.
So, coming back to again evolutionary game
theory is, that the key idea is that in a
population the success of an organism, depends
on how it interacts with other organism.
Notice, that when we started talking about
game theory and also in the middle, we talked
about two different scenario, in which a decision
maker, does not have to worry about the strategic
consideration, there he gets guided by the
parameters like in a market, when you buy
an object typically, when you know you do
not bargain and all you know the prices fixed,
in that case there is no strategic consideration.
But, whenever two players are interacting,
then strategy becomes important.
What happens in the animal world?
The animas interact with each other to grab
food, to grab resources to help them grow
to help them remain fit.
So, the interaction place very, very important
role, so although that interaction is no longer
as strategic interaction, but nevertheless,
there is an interaction.
And, the role of the strategy would be played
by genetic code that will be reflected in
the particular behavior.
So, in the animal world it does not make sense
to measure fitness of a particular individual
organism or particular individual animal.
What we are interested in is, that we should
measure fitness in the context of full population
in which it lives.
How does a particular animal do, we saw we
other animals in the same population that
becomes important.
So, if we think evolutionary game theory is
analogous to our regular game theory, what
do we have, who are the players, the living
organism, animal or living organism, animal
planet they are the players, so organism.
What are the strategies in coded behavior
or characteristics?
What is the payoff?
Payoff is fitness and this fitness should
be evaluated in context of other players.
So, that would be in the game matrix, the
payoff should be, these are region one animal
interact with the other animal, what happens.
Let us take one example to understand this
concept and this is a game that is being played
in the beetled world.
I have taken this example from a very popular
book and very nice book, Networks, Crowds
and Market, which is written by Easley and
Kleinberg.
This example is from chapter 7, you do not
have to read the whole chapter, I have captured
the essential and this is a beetle I have
given the picture of a beetle.
So, what we have this beetle’s fitness depends
on finding and processing food effectively.
Now, let us say that all beetles are of the
same size of this size, let us say this picture
represents the size and there is a mutation
for some reason, some genetic reason.
Now there are some beetles with the larger
body size, imagine a size choice bigger than
or 1.2 times bigger than this size.
Of course, it is safe to assume that a large
beetle will need on average more food in comparison
to a regular or the small size beetle.
So, what should be the consequence of this
mutation this change, that now you have beetle
with larger size.
What should be the consequence?
One thing that one can think, that larger
beetle will on average need more food, so
their fitness would be less than a small beetle
and so that, they would on average do worse
than a small beetles.
So, eventually they will be wide doubt from
the population, why less fitness means they
will be able to, their reproductive success
would be worse than the normal beetle.
So, eventually their pro there proportion
would short decreasing in the whole population
and over the period through the evolution,
they will be wide doubt from the whole population.
But, the question is it, so we will see we
will use game theoretic notion to understand
that and what we are saying that a beetle
typically competes with other beetle for food
it is not like the food getting food depends
on one beetle alones, so the compete with
each other.
So, we are making some assumption, now a large
beetle would get more food on average, because
of their larger size in comparison to a small
beetle.
Then, we can say that, if two if, let us say
that is true all the time, but if there is
a competition between two beetles.
And then, if beetles are the of the same size
on average they will get equal share, they
will be able to divide the whole resource
in equal proportion.
And, if a beetle is large and other is small
in the competition, then the large beetle
get the majority share, because we assume
larger size would help in capturing larger
resources.
But, we should not forget that a large beetle
experiences less fitness in comparison to
a small beetle for the same quantity of food,
why to maintain that metabolic activity in
the body in the larger body, you need more
food.
So, if amount of the food is the same, then
the larger beetle would experience less fitness,
so here is the size game between two beetle
and these numbers are made up adjust to satisfy
all the assumption, that we have made here.
So, what we have, when a small beetle interact
with the small beetle, they both get 6 comma 6
We can assume that the size of resources,
let say 12 and they get half and half, when
there is a large beetle and a small beetle,
then there is a fight some of it get lost
and so large beetle gets 10 and small beetle
gets 1.
And, when to large beetle interact lot gets
last in fight and they both get 4 and 4 and
also for the same amount of food a large beetle
would have less fitness, that would also decrease
this number to 4 and 4 rather than to 6 and
6, so you can justified in two different ways.
Now, what should you also notice, that I do
not need to give the payoff of the second
beetle, if I get rid of this second number.
We, have just you are 6 1 10 and 4, what we
do to get the payoff of the second beetle
the beet beetle number 2 here, and beetle
number 1, here how can we get we just transpose
the matrix, we will get the payoff of the
second beetle, let us transpose it 6 will
be here this one will come here.
This 10 will go here, and this 4 will be here,
so exactly the same matrix we get, and here
is natural selection of force works over longer
times scale.
Now, what do we have, we are going to talk
about new notion, a new concept, a concept
of evolutionary stable strategies the idea
is very simple.
We cannot talk about Nash equilibrium any
more, why because remember, how did, what
is the Nash equilibrium that players are giving
the best response up a player is giving the
best response of all other players strategy
and this is true for all the players.
In, other word also a player would not like
to deviate, player would not like to change
this strategy given, what other player are
doing and the if this is true for all the
player, then we say this is Nash equilibrium.
Here, when we are talking about beetles then
of course, beetles are not changing size they
are they cannot simply this is not feasible
that they would change size.
So, it is not about taking deciding a strategy
concisely or rationally it is just hardwired.
So, what is required here in the evolutionary
biology?
What is required that a genetically determined
characteristics an behavior, we have already
given it a name this is strategy that becomes
stable throughout the population.
What do we mean by becomes stable that if
this is strategy if this particle, if animal
of this particular characteristics are present
in the population, if the same animal with
some other different characteristics get introduced,
they do not has they are not as fit as the
previous one, then only we say that the previous
one is the evolutionary stable one.
In other word, how again, how the new type
would get introduced one process that is present
in evolutionary biology is called mutation
of some changes.
So, this a change would not persist, if there
is a change it would eventually, why doubt,
if a particular characteristics is evolutionary
stable.
So, we are looking for now evolutionary stable
strategies rather than looking for Nash equilibrium.
