Page 6 - Science Focus (issue20)
P. 6

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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