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From YouTube: Game Theory of Developmental Processes
Description
Lecture given for Dynamics Days XL 2021. Virtual and Nice, France. Slides on Figshare: https://figshare.com/articles/presentation/Game_Theory_of_Developmental_Processes/16435308
A
A
A
When
we
talk
about
developmental
game
theory,
we
want
to
talk
about
agents,
I'm
going
to
talk
about
some
definitions
of
agents,
so
the
general
case
is
something
we
call
developmental
agents,
and
so
these
these
developmental
agents
take
the
form
of
cells,
morphogenesis
or
gene
products,
and
you
can
imagine
that
cells
come
in
many
different
types.
Morphogenesis
comes
in
many
different
states
and,
of
course,
gene
products
come
in
many
different
states
as
well,
and
these
all
these
agents
all
limit
states.
A
So,
whether
it's
you
know
it
could
be
between
the
agent
and
nature
or
it
could
be
between
two
agents,
and
so
the
interactions
will
determine
the
game,
and
so
you
can
see
here
sort
of
an
example
of
this,
where
you
have
a
developmental
agent,
where
you
have
this
nondescript
cell.
That
forms
three
germ
layers
and
then
those
three
germ
layers
form
different
parts
of
an
anatomy,
and
this
could
be
some
sort
of
agent
that
behaves
in
the
environment
has
sensors.
A
It
has
a
central
nervous
system
and
it
has
different
body
parts
and
all
those
have
a
developmental
origination,
and
you
can
see
that
they,
you
know
there
could
be
say,
for
example,
a
game
against
nature
or
a
game
between
different
agents
and
there's.
You
know,
competition
cooperation
and
all
those
things.
A
A
specific
case
of
a
developmental
age
is
an
anti-genetic
agent
and
so
not
a
genetic
agent.
It's
an
important
distinction
to
make,
because
ontogenetic
agents
do
not
use
cognition
to
execute
behaviors.
In
the
example,
we
saw
before
all
those
processes
unfold,
but
there's
no
cognition,
there's
no
intention
behind
the
behaviors,
and
this
is
different
from
typical
game
theory.
Like
saying
economics
where
you
have
you
know
rational
strategies
and
things
like
that
where
we
assume
certain
types
of
sub
are
optimal
or
sub-optimal
behavior.
A
In
this
case,
it's
just
simply
strategies
that
are
constrained
by
energetics
or
by
other
factors,
and
so
that's
all
we
assume
so.
Instead,
the
intentional
strategies
that
are
used
in
optogenetic
agents
are
related
to
transformational
processes
such
as
movement,
differentiation,
growth
and
regulation,
so,
for
example,
in
movement,
there's
a
something
that's
generated
by
muscle
and
that
it
generates
in
you
know
an
intentional
state
in
the
sense
that
it's
you
know
definitely
say,
moving
left
instead
of
moving
right,
but
it's
not
cognitive.
A
There's
no
reflex
reflexivity
to
this,
and
so
one
example
of
how
anti-genetic
agents
can
use
this
information,
and
can
you
know
build
themselves.
Some
sort
of
game
is
coordination
between
option
genetic
agents?
So,
in
this
case
you
have
coordination
that
results
from
collective
behavior
over
time
or
you
know
you
could
also
have
perfect
coordination
and
you
can
assume
this
a
priori,
and
so
in
this
case
you
have
a
bunch
of
agents
that
are
cooperating
in
a
game
they're.
A
You
know
they
have
intentional
behaviors
that
are
generated
and
those
behaviors
have
payoffs
and
those
payoffs
involve
some
sort
of
you
know,
energetic
constraints
or
energetic
costs,
and
so
they're
either.
You
know
loosely
or
perfectly
coordinated,
because
the
game
is
such
that
the
payoffs
favor
coordination.
A
So
we
also
want
to
talk
about
developmental
trade-offs,
and
so
we
want
to
model
the
internal
state
of
an
optogenetic
agent
to
show
how
developmental
trade-offs
sort
of
shape
the
execution
of
a
developmental
game,
and
so
in
this
case
we
want
to
consider
that
the
major
any
agent
needs
to
maximally
conserve
energy.
This
is
a
law
of
physics
and
it's
a
law
of
biophysics
as
well,
and
so
an
agent
will
naturally
invest
in
one
set
of
strategies
over
another,
but
it
won't
do
this
intentionally.
A
A
This
can
also
change
the
composition
of
different
agents,
and
this
can
lead
to
heterogeneity,
so
ontogenetic
agents
with
more
available
energy
have
a
greater
degree
of
complexity
with
a
capacity
for
a
greater
number
of
strategies.
So
you
can
see
how
this
process
works.
You
have
these
different
trade-offs
between
heterogeneity
and
homogeneity.
Depending
on
how
much
energy
there
is
in
the
environment,
fitness
could
also
serve
a
purpose
of
energetic
scarcity.
So
if
things
are,
you
know,
there's
a
fitness
imperative
to
keep
the
developing
organism
alive
so
that
it
can
reach
maturity.
A
A
They
look
like
maybe
they're
thinking
or
maybe
they're
they're
definitely
alive,
but
you
know:
what's
driving
this
what's
driving
almost
looks
like
goal-directed
behavior,
and
yet
maybe
it
isn't
exactly
the
type
of
goal-directed
behavior
that
a
human
agent
would
or
some
sort
of
animal
would
pursue,
and
so
here
you
have
like
a
cell
colony,
that's
moving
in
different
ways
and
may
be
oozing
in
in
a
certain
direction
or
it
may
be
moving
in
a
along
some
polar
coordinate
system.
So
you
know
biological
intentionality.
A
A
So
the
first
thing
we're
going
to
talk
about
here
is
zero
player
games
and
so
zero
player
games
an
example
of
which
is
conway's
game
of
life.
So
in
this
game
this
is
conway's
game
of
life.
Over
on
the
left
and
to
the
right,
you
can
see
how
you
can
generate
nd
point
processes
and
dimensional
point
processes,
and
you
can
see
that
this
is
what
we
kind
of
use
in
the
game
of
life.
This
is
a
zero
dimensional
aspect
of
it.
A
Is
this
this
point
process
the
single
point
that
changes
its
state
over
time
and
so
cells
operate
at
a
point
processes
that
emit
a
state
of
debt
or
alive
in
this
game.
So
in
this
zero
player
game,
you
have
a
an
autogenetic
agent,
it's
operating
as
a
point
in
space
and
it's
emitting
the
state
of
dead
or
alive.
So
there's
there's
no
real.
It's
just
generating
the
state.
It's
not
really
interacting
with
other
players.
A
A
There's
a
life.
There
are
a
lot
of
lifelike
attributes
captured
in
these
dimensions,
but
there's
no
real
competition
here.
So
this
is
an
example
of
a
zero
player
game,
and
if,
in
applying
this
to
development,
we
can
look
at
things
like
turing,
morphogenesis
or
reaction
diffusion
processes,
where
particles
compose
a
population
of
zero
dimensional
agents
and
what
they
the
sort
of
substance,
they
call
morphogens
act,
indirect
way
to
transform
populations
and
a
spatial
pattern.
A
An
equilibrium
is
reached
when
a
stable,
morphogenetic
morphogenetic
pattern
is
achieved
so
under
developmental
game
theory
that
we
can
reach
equilibria
just
like
we
can
in
normal
game
theory,
but
it's
a
little
bit
different
in
terms
of
the
sort
of
where
this
limit
is
so.
This
is
an
example
of
a
very
simple
payoff
matrix
for
a
zero
player
game.
Within
this
payoff
structure,
the
cell
will
tend
to
stay
alive
and
you
can
see
the
payoff
structure
is
0.8
for
alive
and
0.2
for
dead.
So
when
the
payoff
is
high
for
being
alive,
it'll
stay
alive.
A
A
A
A
So
in
this
case
an
ontogenetic
agent
will
play
an
intentional
strategy
against
the
quasi-random
natural
process,
so
quasa
quasi-random
natural
process
is
something
like
weather
or
entropy,
and
so
the
payoff
structure
here
will
be
solely
dependent
upon
a
process
driven
objective
so,
for
example,
an
increase
in
fitness
or
a
maximum,
a
maximization
of
error,
correction
and
the
actual
application
and
development
here
we're
going
to
get
into
is
a
generic
developmental
process
that
we'll
talk
about
as
a
game
of
developmental
minesweeper
and
so
again
just
to
go
over
this.
This
example
with
the
weather.
A
This
is
a
game
against
nature.
This
is
a
single
rational
player
ping
playing
a
pure
mixed
strategy
against
nature,
which
is
a
random
or
mixed
strategy.
So
a
strategy
in
this
case
is
carrying
an
umbrella
or
not
carrying
an
umbrella
in
when
the
weather
is
changing
all
the
time.
So
you
have
a
weather
forecast
here,
and
the
weather
forecast
is
generated
by
a
discrete
discrete
random
random
pattern
generator.
So
it's
generating
these
patterns
of
weather
and
the
forecast
that
we
make
is
imperfect
information.
A
So
the
question
is:
is
that
the
observer
do
they
have
to
carry
an
umbrella
or
not,
knowing
that
the
weather
is
always
changing
and
that
the
forecast
is
imperfect
information?
So
you
can
see
that
the
observer
strategy
here
is
below
your
end.
It's
an
umbrella
or
no
umbrella,
and
the
payoff
is
whether
you
have
an
umbrella
and
it
rains.
A
If
there's
you
know
it
doesn't
rain
and
you
have
an
umbrella,
there's
no
payoff
and
there's
a
positive
payoff.
If
you
don't
have
an
umbrella
and
it's
sunny
because
you
don't
have
to
carry
the
umbrella
with
you.
So
you
can
see
that
there's
this
case,
where
you
don't
have
an
umbrella.
You
get
a
negative
one
payoff
because
you
get
soaked
in
the
case
where
you
do
have
an
umbrella
and
it
rains
you
get
one.
A
So
this
is
this:
has
a
nice
connection
with
something
like
reinforcement
learning,
because
it
does
reward
the
agent
with
every
sort
of
correct
guess
of
what
nature
is
going
to
generate,
and
so
just
keep
that
in
mind
for
right
now
and
then
you
know
think
about
that
in
terms
of
the
game
against
nature,
in
this
case
we're
going
to
look
at
a
very
specific
case,
and
this
is
the
developmental
minesweeper
game.
So
this
is
a
picture
of
the
classic
minesweeper
game
on
the
right
and
minesweeper
is
a
game
between
nature
and
a
single
autogenetic
agent.
A
So
the
ontogenetic
agent
is
doing
the
job
of
the
player
one
in
this
minesweeper
game,
they're,
uncovering
different
they're,
selecting
different
tiles
and
I'm
covering
a
piece
of
this
landscape
and
the
idea
is
you
can't
select
where
there's
a
the
place
where
there's
a
bomb
or
a
mine,
because
you'll
blow
up
and
you'll
your
game
will
be
over.
So
the
idea
is
not
to
pick
a
spot
where
there's
a
mine
and
you
get
as
much
of
the
board
uncovered
as
possible,
and
so,
if
you
can
uncover
every
square,
but
the
squares
were
their
minds.
A
You
win
the
game,
and
so
you
can
actually
take
this
game
and
turn
it
into
a
developmental
game.
By
looking
at
this
game,
where
you're
created,
you
have
a
two-dimensional
genome
mandan,
this
is
a
two-dimensional
genome
and
the
algorithmic
agent
doesn't
know
where
the
mines
are.
In
this
case
the
mines
are
lethal
mutations,
so
the
agent
is
picking
spots
in
the
genome
and
some
of
these
are
lethal
mutations.
So
the
idea
is
that,
in
this
two-dimensional
space
the
agent
is
picking
places
to
sort
of
express
its
genome,
but
it's
not
picking.
A
It
doesn't
want
to
pick
the
lethal
mutations.
It
wants
to
pick
around
that,
and
so
the
idea
is,
these
are
generated
by
random
processes,
and
the
agent
has
to
sort
of
predict
where
there's
not
a
lethal
mutation,
but
it
has
no
information
as
to
what's
a
lethal
mutation.
So
that's
the
idea
here
and
so
these
null
squares
it's
interesting,
because
this
game
has
a
fairly
high
degree
of
a
set
of
degrees
of
freedom.
So
it's
actually
a
fairly
large
search
space,
and
so
we
can
also
add
another
information
to
be
uncovered.
A
A
So
in
this
case
we're
going
to
look
at
the
game
tic-tac-toe
and
it
seems
like
a
pretty
boring
game,
but
it
actually
has
a
lot
of
nice
properties
for
this.
So
there's
actually
in
tic-tac-toe,
something
called
a
first
mover
advantage,
and
this
is
where,
if
you
pick
like,
say
the
center
square,
if
you
start
the
game,
you
can
always
be
on
the
offensive
and
your
opponent
has
to
be
on
the
defensive
if
they
want
to
play
an
optimal
game.
A
A
This
is
where
you
have
optimal
play
by
the
onto
genetic
agents,
plus
this
first
mover
advantage
of
one
cell
lineage
over
another,
and
so
this
means
that
there's
no
clear
winner.
So,
for
example,
you
know
one
cell
lineage
can't
take
over
the
embryo,
but
on
the
other
hand
you
have
the
structure,
this
semi-hierarchical
structure
of
the
embryo,
something
you
might
even
call
heteroarchical,
and
so
no
one
selena
type
of
cell
dominates
the
embryo,
and
so
the
idea
is
that
you
know
if
you
had
these.
A
So
here
you
have
an
example
from
a
paper
from
biosystems
from
2018
that
we
put
out.
This
is
an
example
of
this.
This
first
mover
advantage
in
tic-tac-toe,
and
then
here
we
have
this
in
the
embryo,
so
you
have
the
cell
one
and
cell
two
cell
one
moves
first
by
dividing,
and
so
they
have
this.
They
they're
able
to
maintain
the
spacing
and
then
two
divides
they're,
the
second
player
they're
playing
this
defensive
move
so
that
one
doesn't
invade
their
space.
A
This
is
in
the
third
move
in
the
fourth
move,
the
psalm
lineage
one
divides
again,
so
you
have
three
cells
versus
two
cells
and
then
the
fifth
move,
the
cell.
Actually
in
this
case,
solenage
one
divides
again,
so
you
have
four
cells
in
one
versus
two
and
two:
the
sixth
move,
lineage
two
divides
into
from
one
cell
to
two
cells,
or
actually
you
have
three
cells
at
that
point.
A
The
idea
here
is
that
you're,
mostly
playing
optimally,
although
you
can
see
examples
where
there's
a
sub-optimal
move
where
lineage
one
divides
twice
and
two
moves,
and
so
it's
able
to
you
know,
structure
the
embryo
in
a
certain
way.
So
if
we
model
it
using
this
first
mover
advantage
model,
we
can
see
that
in
some
cases,
they're
sub-optimal
moves
by
some
of
the
lineages.
A
In
some
cases
both
lineages
play
optimally,
and
we
can
then
use
that
extend
that
result
to
look
and
see
what
exactly
you
know.
The
structure
of
a
of
an
embryo
looks
like
the
structure
of
a
developing
organism,
looks
like
and
maybe
explaining
why
some
of
these
things
are
asymmetrical
or
become
asymmetrical
over
time,
and
so
this
embryo
can
be
analyzed
using
a
first
mover
stackelberg
game,
there's
an
advantage
in
terms
of
size
so
for
differentiated
tissues.
A
Sublineages,
one
and
two
are
established,
and
one
in
this
case
clearly
has
a
size
position
advantage
and
the
second
move,
of
course,
sub
lineage
one
divides
and
then
before
two
and
that's
an
advantage
to
sublineage
one
and
then
the
third
move
supplement
h2
divides,
and
that
gives
a
sublineage
two.
It's
able
to
maintain
its
foothold
in
its
space
in
the
embryo
and
then
the
fourth
move
and
then
so
on
and
so
forth,
and
so
you
can
actually
do
the
same
type
of
analysis
or
have
the
same
type
of
game
for
connectome
formation.
A
If
you
want
more
information,
you
can
go
to
the
paper,
but
these
just
basically
explain
how
these
kind
of
these
connectivity
patterns
are
established
and
what
we
should
expect,
maybe
in
a
more
complex
connectome,
then
we
go
to
something
else.
In
two
player
games,
another
type
of
two-player
game
called
the
prisoner's
dilemma
or
the
iterated
prisoner's
dilemma.
So
this
gives
you
individual
versus
group
incentives.
A
A
So
in
the
case
where
you
have
two
anti-genetic
agents,
they
can
either
cooperate
or
they
can
defect
or
not
cooperate,
and
so,
when
you
defect
it's
to
seek
maximization
of
an
individual
payoff
which
is
often
sub-optimal,
but
it
just
maximizes
the
individual
payoff,
for
whatever
reason,
so
you
know
in
the
case
of
the
antigenic
agents,
they
might
not
cooperate,
they
might
end
up.
You
know
individually,
you
know
benefiting
in
the
short
term,
but
then
the
entire
colony
might
die
out
in
as
a
consequence
of
that.
A
So
that's
what
I
mean
by
sub-optimal
in
the
case
of
the
the
first
first
mover
games.
Of
course
this
does
not
apply,
but
this
is
specific
to
this
type
of
game.
If
you,
however,
cooperate
instead
of
defect,
it
maximizes
the
pairwise
or
group
payoff.
So
in
that
example
of
the
cooperating
agents
they
all
basically
are
behaving
in
the
same
way
and
they're
cooperating
and
it's
maximizing
their
group
payoff.
So
now
the
colony
is
the
thing.
A
That's
surviving
and
maybe
some
individuals
die
off
as
a
consequence,
but
the
colony
survives
in
the
iterated
prisoner's
dilemma.
It's
just
an
example
of
this.
This
example
up
in
the
upper
right,
the
prisoner's
dilemma:
it's
just
that
the
game
is
repeated
dynamically
over
time.
So
you
have
this
repeated
game
that
that,
where
the
payoffs
might
change
over
time,
but
you
get
this
function
that
shows
basically
the
same
trend
where
you
know
the
payoffs
for
defecting
and
the
payoffs
are
cooperating,
might
change,
but
you
can
get
clear
strategies
over
time
and
an
application
of
this.
A
The
development
is
where
you
have
a
pair
of
ontogenetic
agents
with
complementary
mechanisms
such
as
pattern,
recognition
and
so
where
I
meant
to
put
pattern,
recognition
and
pattern
generation
in
there,
but
I
think
I
had
it
both
words
twice.
So
this
is
an
example
of
what
I
mean.
So
this
is
the
observer
in
the
emitter,
and
so
this
is
a
game
that
we
have.
A
We
call
it
a
morphogenetic
game,
and
this
is
where
you
have
the
observer
that
reconstructs
the
pattern
through
perception
from
the
emitter
which
produces
a
pattern,
so
one
exhibits,
morphogenesis
and
the
other
exhibits
perception
or
attention,
and
so
these
two
agents
will
compete
against
one
another,
and
so
this
is
answering
the
question.
What
is
the
relationship
between
morphogenesis
and
perception,
if
you
have
say,
for
example,
an
oxygen
genetic
agent
that
forms
stripes
and
they're
doing
it
to
avoid
prey
or
some
other
reason,
then
what
is
the
relationship
or
avoid
predators?
A
Then?
What's
the
relationship
between
the
predator
and
the
prey?
That's
what
we're
trying
to
maybe
ask
here
one
of
one
of
the
possible
questions
we
could
ask
using
this
model.
We
can
treat
this
as
either
a
predator
prey
relationship
or
a
competitive
cooperative
game
depending
on
you
know
what
relationship
the
observer
and
emitter
have.
A
Some
of
this,
you
know
involves
things
like
peridolia
or
camouflage
and,
of
course,
in
peridolia.
This
is
the
evolution
of
perception,
morphogenetic
morphogen,
morphogenetic
mechanisms.
This
is
the
co-evolution
of
those
in
camouflage.
You
have
this
something
called
a
matching
pursuit
game
which
is
a
different
type
of
game
altogether
and
also
is
part
of
this
developmental
game
paradigm,
and
so,
in
this
case
the
predator
hunts,
the
prey
and
the
prey
must
conceal
itself
or
the
prey
is
dangerous
to
the
predator.
A
In
some
way
like
say
it
kills
with
venom
and
all
those
possibilities
can
be
replicated
in
this
game.
So
in
this
case
we
have
a
pursuit
of
asian
game
which
is
distinct
from
a
prisoner's
delima
game.
In
this
case,
the
observer
tries
to
identify
partial
phenotypes,
while
the
emitter
tries
to
conceal
its
phenotype
as
a
coherent
pattern.
So
here
you
can
see
that
actually,
this
emitter
isn't
trying
to
conceal
its
pattern,
but
it
could
definitely,
you
know,
have
different
types
of
striping
patterns
over
time.
So
you
know
we
have
like
in
the
first
iteration.
A
You
might
have
this
striped
pattern
in
the
second
iteration.
You
might
have
this
checkerboard
pattern,
but
this
other
agent
that's
trying
to
identify.
The
pattern
is
then
going
through
a
series
of
patterns
possible
patterns
to
sort
of
figure
out
which
pattern
it
is,
and
you
know
there
are
a
lot
of
things
here
to
do
with
like
spatial
orientation
and
translation.
So
you
know
this.
This
pattern
might
be
at
an
oblique
angle
in
the
environment,
and
the
agent
still
has
to
be
able
to
recognize
it.
A
So
if
the
agent
can
recognize
that
pattern,
the
payoff
for
that
pattern
is
much
lower
than
it
otherwise
would
be
if
it's
a
unique
pattern
that
the
agent's
never
seen
before.
That's
also
a
very
high
payoff
pattern
for
the
emitter
and
and
so
on
and
so
forth.
So
it
relies
on
the
learning
of
the
observing
agent
and
the
ability
to
generate
patterns
on
the
part
of
the
emitting
agent,
and
so
you
can
see
this.
A
There
are
interesting
connections
between
this
pursuit
of
asian
utility
function
that
you
use
in
a
pursuit
of
asian
game,
and
this
is
a
series
of
iterative
payoffs.
Like
I
said
you
know
these
games
change
over
time,
depending
on
the
pattern,
that's
being
emitted
by
the
emitter
and
depending
on
what
the
observer
has
seen
before,
can
learn
or
can
identify
in
different
contexts.
A
You
have
a
situation
where,
given
a
number
of
perturbations,
a
status
strategies
can
be
found
to
return
the
system
to
an
initial
state
and
resist
invasion
by
mutant
strategies,
and
so
in
the
developmental,
stable
state
case.
It
might
work
in
a
similar
manner
and
it
might
mimic
something
called
the
canalization
of
development,
which
was
proposed
by
conor,
ed
waddington
and
on
the
right.
You
can
see
an
example
of
the
canonization
of
development.