Brotherhood -- In A John Woo's Way

Game theory is the funnier part in economics.

Have you seen "The Good, The Bad And The Ugly"? It is a classic cowboy film starring the invincible Clint Eastwood. In the climax, the good guy, the bad guy and the ugly guy stand in a circle, each holding a gun. All want to shoot one another.

If you were Eastwood, what would you do? Will you be the first to open fire?

Let's jump to a John Woo action film, any one of them. There must be a plot in which two heroes point guns at each other. Would you be the first to pull the trigger, if you were the hard-boiled Chow Yun-fat?

These were no games. They were dead-or-alive situations.

The Eastwood "trio" plot was very clever. The only way to get out of this situation unwounded, if you cannot shoot both the others all at once, was to be the second one to shoot. All three guys paused, and waited for any one of the other two guys to shoot first.

The best strategy is to pray for the possibility that the one who opens fire doesn't aim at you and shoot that guy once he fires the bullet toward the third guy. No matter what, the first who opens fire must die. Everyone knows that and therefore no one wants to shoot first. The most probable outcome is that all three guys stand still and nothing happens forever, although the film had to have an ending.

The John Woo's "duel", the "gun-to-the-head" situation, is different. Who pulls the trigger first will live. It would be too late if you let the other pull the trigger first. The best solution would be to shoot immediately. However, if the heroes do that, the stories would be much shorter than 90 minutes, and tasteless, and Woo would not be the beloved director that he is.

In most of the time in this "gun-to-the-head" situation, the two heroes are good friends, "brothers", or at least, they respect each other, although there must have been some betrayals or revenges.

As the "gun-to-the-head" gestures go, the audience gets thrilled and Woo keeps us guessing: "Who will shoot first? Will the brothers kill each other?"

But i can predict that, once the first second has gone and there has not yet been any shooting, there will be none.

Let's split the long-holding gesture into seconds. The strategy is like this:
(1) If your opponent shoots in the next second, you better shoot now.
(2) If your opponent does not shoot in the next second, you better not shoot. He used be to your "good brother". You look for a live/live outcome, although you put your own life on the top priority. At least, holding the fire saves you from troubles and future revenges against you.

Your opponent has the same idea.

Once the first second has past, you know that your opponent expects you to hold fire in the next second. And your opponent knows your same expectation too.

Trust was built after the first second. The two heroes would hold their positions, keep staring at each other and start talking about their past battles and struggles. i believe Woo has a message on killing as well as not killing. And it was often the latter that struck me.

Trust, or, put it in a more romantic word, brotherhood, does make better returns. In the money world, cheating would work for quick profits only.

In a classic prisoner's dilemma, a game, which requires two players operate with each other to get the best outcomes, each of the two players will cheat because:
If the other cheats, he had better cheat to avoid the greatest suffering; and
If the other doesn't cheat, he would still rather cheat to exploit the benefits.

The game suggests that people are so cruel, provided that the game is played only once.

But if the game has an unpredictable number of rounds, the best strategy is to operate in every round of the game. It is because, if a player cheats, he will lose the benefits from operation in the future rounds. This can be applied to our daily lives as to how we can operate with other people to get better results.

In a world that has a finite lifespan, the situation would be like the blind survival game in Kinji Fukasaku's movie "Battle-Royale". Fortunately, we have a future and hence there are reasons for brotherhood.

Apr 27, 2005
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