Game Theory

Game theory is a branch of applied mathematics, but strangely, discussions about it came during our literature lesson, and sparked off an animated debate.


It all began when one of our Prelim-exam articles, Kaff's short story "Survivor", grabbed our attention by its unique ending.

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A man and his sleigh dog were marooned on an iceland near the South Pole. Their fates were sealed if there was no plane to save them within one week. The man's survival prospects were bleak in the face of the harsh weather and the menace from the only living thing beside him--the dog.


For fear that his dog, a huge one, would overpower him and eat him up to avoid its impending starvation, he chose to act first. He began to hone a knife. The dog gazed at him curiously and the man believed that he saw fear crossing its face, but he went on his mission--facing the threat of death, no one could be altruistic.


He ordered the dog to come to him, and lifted the shiny knife.


The dog obeyed, albeit it flinched at first.


He was overcome by his conscience and threw the knife away the moment his dog approached him, and cried in the snow.


That was when the dog knew.


It circled around the man, hollering and bawling menacingly with its last strength. The man continued to whimper.


The dog stopped to lick his face with its warm, wet tongue, and the man who had been thrilled to bits, went up to hug the dog, tightly.


Two days later, an aeroplane circling around the area observed a shiny spot in the whiteness of the snow and spiraled down.


It was the knife.


So they were both saved, the man and the dog.
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The discussion was: if you were the man, would you kill the dog?


Some answers came within seconds:


"I won't. I don't eat raw meat. It was disgusting."


"No. Of course. I can't bear the thought of killing anything."


"Maybe...No, should not be...If it dare come near me I would kill it for sure."


"Yeah, I will hone a knife...but it depends whether I kill the thing..."


My answer:"No. Of course. My strength enough to kill a dog? Joking! I can't make it die even if I kill it, so why bother?"


The essence of the discussion, however, was not what we have discussed above. So our devastated teacher(after hearing our answers, especially the "no-disgusting-raw-meat" answer), envisioned a new situation.
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If all of you are arrested by a terrorist who divide you into two groups in different buildings and he gives each group a control pad that controls the bombs of the other group's building. If you denotate the others' building, you will be released alive. However, if the other group acts first and decides to bomb your building, you will die. Each group has three minutes to decide which action to take...

Will you press the "red button" of your controller?

We were literally divided into two groups in my class that were supposed to be put in the two buildings, and the three-minute discussion started. Within three minutes, we were supposed to message our teacher our mutual decision whether to "bomb" or not.

At the end of the three minutes, neither side pressed the "red button", so we both survived.
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In reality?

With people you do not know in the other building?

Both groups will bomb the other side, but the group I was in pressed the button first so the other group died.

With your family members in the other building?

Neither pressed the button.

With possible criminals?

For sure we both "bombed" the other side, but again there was the "time issue". Our group sent the message faster so the other side was blasted into oblivion.
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Mr. Cai(our literature teacher) came into a conclusion based on our reactions: if there are people we know, we won't bomb the building, but if they are strangers, off they die.

So he made the situation more complicated.

Inside the other building: 1 family member, 19 possible criminals. Bomb?

"Hmm...then..."

Inside the other building: 20 family members / friends or 20 possible criminals. Bomb?

"Uh-huh...well..."

Inside the other building: you don't know who they are, and how many of them. Bomb?

"Gosh! I quit!"
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"Wait, who are in MY building with me," I asked Mr. Cai.

"Your friends and family members."

"Then I will bomb them."

"What if you are with people you do not know?"

"Then... I won't press the button, and persuade people in my side not to. But if they do insist, I have nothing against it, either. The decision is beyond me, now."
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"So it depends on your 'fate'~" (everything seems to be about fate and luck...don't say it about exam:)
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We roared...Mr. Cai is a hardcore fatalist, so whenever we come to this topic, we feel like treading on landmines. Here he came...

It is actually a model of "game theory", in fact a situation of Nash Equilibrium (Note: John. Jr.Nash was the Nobel laureate for Economics due to his contribution to 'equilibrium concepts', and I have read a biography about him).

Nash Equilibrium:
If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium model.

Upon searching more into the topic, I made an appalling dscovery that Game Theory is also applied in the study of biology, in a concept called "biological altruism".

Biological Altruism:
A situation in which an organism appears to act in a way that benefits other organisms but is detrimental to itself. This is distinct from traditional notions of altruism because such actions are not conscious, but appear to be evolutionary adaptations to increase overall fitness of the species.

Examples:
Vampire bats, who regurgitate blood they have obtained from a night's hunting and give it to group members who have failed to feed.

Worker bees, who care for the queen bee for their entire lives and never mate,

Vervet monkeys, who warn group members of a predator's approach, even when it endangers that individual's chance of survival.

All of these actions increase the overall fitness of a group, but occur at a cost to the individual.
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Then I realise. "Game theory" is much more complicated in real-life application and many factors around you, coupled with your own choice and decision, will decide your fate.

Then it dawned me on the Cuban Missile Crisis:

What if either John.F. Kennedy or Khrushchev chose to press the "hot button" during the Cold War? A nuclear war?

Thank goodness they steered away from it...

Maybe they both knew well about the "game theory". Who knows? But thank goodness if they knew.