Page 6 - Science Focus (issue20)

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By Sonia Choy 蔡蒨珩
People are, in a nutshell, quite depressing. Even When the game is repeated, the optimal strategy
though when we know we need to cooperate might not be always cheating. For example, you
with each other in order to do something, from an could alternate between cheating and cooperating,
assignment to stopping global warming, people just at random, or repeat what your opponent does to
can’t help but act out of their self-interest and prevent you in the next round. You have the choice of pure-
the best case scenario from happening. But why is this strategy (sticking to a certain plan on what to do) or
the case? Game theory, a branch of mathematics, mixed-strategy (i.e. using a bit of probability) tactics
might give you a few answers. [2]. For the sake of our sanity, we’ll reword the game
by asking players to bet points and awarding marks to
We first look at a one-off game which goes like this; each player instead – prison terms don’t really add up
imagine you are a prisoner with a prison guard baiting properly, and we are now able to deduct points.
you to tell on your good friend (who is also in prison).
If you both stay silent, then they do not have enough They cooperate They cheat
evidence, and you both get your sentence of a year; if (bet 1) (bet 0)
only one of you confesses, the other gets punished with
three years in prison, while the teller walks free; if both of You cooperate You get: +2 You get: -1
you confess, you go to prison for two years. The catch: (bet 1) Opponent gets: +2 Opponent gets: +3
you cannot communicate with your friend throughout
this process. In this scenario, what will you do? You get: +3 You get: 0
This is the infamous prisoner’s dilemma, in which if You cheat
(bet 0)
you act to protect your self-interest, you prevent the best Opponent gets: -1 Opponent gets: 0
case scenario. Any sane person will betray their friend,
because if your friend cooperates and you cheat, you If you don’t want to dive into the math, we can
walk free; if your friend cheated, it is definitely better for chuck this scenario into a computer program (footnote
you to cheat, since at least you get out of prison a year 2) and repeat it multiple times to see what happens:
earlier. The best scenario here, however, is if both of you what ultimately emerges as the victor in this game is the
stay silent and get out of prison together after a year. strategy of repeating your friend’s last play. The ancient
But your fear of being betrayed (or rather, your desire to Chinese wisdom of “do unto others as you would have
walk free) prevents this from happening. done to you” seems to hold up here – if you want to win,
cooperate since you want your opponent to cooperate
They cooperate They cheat as well, and if your opponent follows the strategy of
repeating your friend’s last play, you two will always
You get: 1 year You get: 3 years cooperate and achieve the best outcome.
You cooperate This, though, is quite an idealized model. In the real
Opponent gets: Opponent gets:
1 year freedom world, people make mistakes, and blunders occur.
You get: freedom You get: 2 years What happens when you follow a strategy that is
You cheat bound to make you win in theory (that is, repeating
Opponent gets: Opponent gets: your friend’s last play), but your opponent occasionally
3 years 2 years makes mistakes on which option they choose? Now we
go back to our simulator – among a crowd of generally
These games always have an “equilibrium point”,
known as the Nash equilibrium (footnote 1) – the point distrusting opponents who have a 5% chance of making
a mistake (50% will always cheat, and the rest are a mix
where both players are satisfied with their outcome, of different strategies), we realize that the strategy of
enough to stop them from switching to another strategy cheating only if your opponent cheats twice in a row
[1]. In that situation, the game has arrived at its optimal will win you the game. However, as distrust increases,
outcome, known as the value of this particular game. the winner of the game will be the character that
So here we will actually have a certain “best” solution to always cheats no matter what – the sad truth. This shows
the game – we say that the dominant strategy here is to the importance of clear and accurate communication;
cheat. However, it does not give the best outcome.
a little bit of miscommunication will lead to forgiveness;
But in life, we constantly make decisions; what however, more and more mistakes will lead to widespread
happens to this game if it happens more than once? distrust [3].
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