Game Theory: Winning the Game of Life
are you the type of person to analyze
every second of the interaction you just
had with someone for hours on end or
are you normal either way you probably
don't think all that hard about every
single detail of the decisions you make
in social situations
but believe it or not there's an entire
scientific field that applies to social
situations and decision making
we're talking about game theory game
theory can be used to analyze both
economic and social situations
it's essentially the science of strategy
and just like the reality it is trying
to model
game theory can get really complicated
and yes
although game theory is relevant to
games as we typically understand them
such as poker most research and game
theory focuses on how groups of people
interact
let's first define what a game is so
what exactly is a game
it sounds like a stupid question like
who doesn't know what a game is
but games in the field of game theory
are a slightly different concept to what
you might expect
when it comes to game theoretic analysis
the game constitutes any interaction
between multiple people where each
person's payoff is affected by the
decision made by others
let's apply this definition of a game to
a couple of
games is sudoku a game well
in the traditional sense sure but in
game theory
no sudoku is not a game sudoku is not a
game because how you decide to complete
the puzzle doesn't affect any other
player
there is after all only one player in
the game
you what about tic-tac-toe is that a
game
two players can play the game and each
box that is filled by one of the players
affects the other player
winning requires both players to respond
optimally to what the other player is
doing so yes
it is a game you could also have a
situation where two shop owners choose
from a finite number of positions where
to strategically place their shops for
maximum profit
they are each affected by what the other
person does since they may be opting for
the same market
and there's certainly a win-lose
situation here so
even though placing your shop may not
sound like much of a game
in the eyes of game theorists it
certainly is
game theory is the study of games like
these and game theories try to model
games in a way that makes them easy to
understand and analyze
i say easy but a lot of games can end up
having pretty similar properties or
reoccurring patterns
and more often than not things can get
pretty complicated
game theory has two main focuses
cooperative games and non-cooperative
games
most game theory models involve five
conditions it goes something like this
first each player has two or more
choices or sequence of choices
think of these like typical moves in a
game like moving a chess piece
second all possible combinations of
decisions or plays result in a clear
outcome
basically you can win or lose third
it's clear how you can win or lose and
participants will gain or lose something
depending on the outcome
fourth the players know the rules of the
game as well as the payoffs of other
players
meaning everyone is aware of what is
desirable to the other players as well
and fifth the players are rationable and
sensible people
rational here means strictly that when
they're faced with two alternatives
they'll choose the option that provides
the greatest benefits while players know
the rules and their opponents options
they don't know their opponent's actual
decisions in advance
so players must choose options based on
assumptions of what their opponents
might choose
some game theory scenarios are zero-sum
games meaning one player's win is
another's loss
and vice versa others however
allow mutual gains and losses these
games can involve multiple strategies
you can try to minimize the maximum
losses another player can cause and make
decisions based on probable outcomes
this all really just sounds a bit
confusing so here just let me show you
if life is indeed a game then the first
rule is to be skeptical of other
people's suggestions
as we said if it's a game someone else
is going to be competing
so there's definitely going to be
competition and sabotage
perhaps a straightforward and well-known
example is the prisoner's dilemma
the game goes like this two criminals
are caught red-handed and are arrested
each has two choices they can each
either stay quiet
or testify against their friend upon
arrest
they are each separated and offered a
deal testify against your friend
and will let you off the hook easy with
one year in prison and give the other
person 10 years
if both stay quiet the cops can't really
prove the more serious charges and both
criminals would spend only 2 years
behind bars
if they both testify against each other
however then both would get 5-year
prison sentences
at first glance keeping quiet seems like
the best strategy
if they both did this they would both be
out after just two years
but right before they're about to
testify one of the two thinks to himself
what if i stay quiet and the other guy
rats me out without knowing what the
other person is actually going to decide
it's a reasonable worry to have the
smartest solution to this would be to
react in a way that is beneficial
regardless of what the other person does
a nash equilibrium is actually a state
in which no one person can improve given
what the others are doing
this means you're picking the best
response to a particular strategy from
your opponent
a quick analysis of the prisoner's
dilemma reveals they would both most
likely testify
which is the nash equilibrium for this
problem this is because regardless of
what the other person does
testifying will lead to a maximum
sentence of 5 years with the potential
for a 1 year sentence
meanwhile if you don't testify you could
end up with a 10-year term
it's easily the safest thing to do
considering neither party knows what the
other is going to do
even though both criminals are better
off if they just stayed quiet
here the individual incentive wins over
group interest
testifying is a better option because
you know that you'll be in trouble if
you stay quiet but your friend testifies
but if you can think of that your friend
can too
so he knows you're likely going to
testify given that it's the safer option
for you
and you know he's likely going to
testify too for the same reason
and you know that he knows that you're
likely going to testify
you see the loop that's forming these
types of problems are examples of
non-cooperative games
which means the two prisoners can't
convey their intentions to each other
if they were able to talk to each other
however we would be in a cooperative
setting
and that would affect the likelihood of
certain outcomes as you can imagine
for example it'd become much easier for
them to agree beforehand that they're
both just going to stay quiet
on the contrary a coordination game is
one in which everyone benefits from
working together
there's no incentive for either party to
cheat since it will result in a worse
outcome than if they just cooperated
a good example is driving on the correct
side of the road you win nothing by
driving on the wrong side of the road
but sometimes you lose without even
playing
the principal agent problem is when one
person is allowed to make decisions on
behalf of another person
in this situation the first person is
likely to prioritize their own interests
and pursue their own goals
and well yeah that's the basis of modern
politics
game theory can also be applied to
biology though in fact
its application in the field of biology
has allowed biologists to answer a lot
of questions about evolution
which is remarkable since game theory
was never designed for this
for example it's helped scientists
explain biological altruism
where an organism acts in a way that is
most favorable for the overall species
even if that action is harmful to itself
a bird might warn the rest of the group
about the arrival of a predator
doing so risks its own life since it
essentially announces itself to the
predator
but this trait can later help that bird
assuming it survives of course
when other birds return the favor and
worn it these concepts might help you
anticipate some of the strategies others
might be using to get one over on you
but who really knows what they're
thinking the concept of guessing others
moves is what makes the game so tricky
while each player is likely to be
certain about only their own move they
still have to speculate about other
players decisions
and more importantly other players
conception of every other player's
decisions
essentially you are no longer making a
decision based on what you think is
right
rather you're anticipating what your
opponent thinks is right and simply
reacting to it
but then again your opponent is doing
the same exact thing
so who's really making the decision here
whose mind is the actual decision being
made in
let's put it another way each player
must know their own chance of coming out
on top
guess everyone else's chance and also
guess what everyone else is guessing
about their own chances of winning
not only this but you also really need
to be able to guess what other players
are guessing about your guesses about
them
and now look we're confused again
another problem is that
although game theory has many benefits
it would be impossible to properly apply
it in all situations
there will be times where rationality
might not offer the right solutions
or a mutual benefit might not be the
most ideal outcome
when you come up against these you have
to not only recognize them
but then also decide whether using game
theory would be the most helpful way to
deal with the situation
by then the moment could already be gone
the assumption that everyone is going to
be rational a basic premise of game
theory
is also a really risky one humans can be
extremely unpredictable and emotional
and this makes the guessing work near
impossible
there's a ton of real-life examples that
illustrate the basic concepts of game
theory
apple and samsung are involved in an
endless game of advertising
it's not like either company needs to
advertise besides advertising can get
extremely expensive
so why not just forego this task all
together and use the money for research
and development
if both companies did this then we'd
probably have better phones by now
but sure enough apple banks on the
possibility of samsung advertising and
gaining an edge over the market
and samsung does the same and that
possibility soon turns into a certainty
you and i have all come to accept
now this is an extremely simplistic
example that bypasses many other
variables
but you see the basic concept another
good everyday example can be found in
the treatment of public goods and
property
if everyone decides to be good citizens
and not litter society benefits as a
whole
but you're inevitably going to come up
against one or more people who choose to
essentially go rogue and behave
selfishly by littering
this leads to society as a whole bearing
the cost of cleaning up
all the while making not littering a
less worthwhile decision
after all if the road's already littered
the work to not litter is that much less
meaningful
you can probably now see how applicable
this is to other situations in life
like every big important decision we're
supposed to be fixing
but more on that later as interesting as
it is
game theory can still only analyze
simple situations with well-defined
constraints
and you must remember that any model is
a subset of reality no matter how good
it is
it's essentially intellectual guesswork
the bottom line
we're all constantly in the game it's
pretty impossible not to be
our lives are endlessly and unavoidably
impacted by the actions and decisions
made by others
so you might as well play the game the
best you can
and that interaction you spent hours
analyzing after the other person has
already long forgotten it
maybe it's not such a bad thing after
all we're just trying to win the game of
life
and the reason to win is so that you can
be free of it
game theory is complicated and i don't
think it's something you're consistently
aware of
it takes time to truly understand and
there's even more scenarios than just
the ones i've mentioned that you'll
encounter pretty often
it has roots in mathematics statistics
and probability
if you're interested in things like this
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theory they're here to help you with
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