Home » Opinion » Book review
On paper, stone, scissors, and earwigs
By Wu Jiayin |
November 28, 2009, Saturday
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Print Edition
Print Edition
BOOKS on mathematical theories tend to be abstruse and full of jargons and equations.
But not the entertaining "Rock, Paper, Scissors" by Len Fisher, which elucidates game theory and its wide applications with vivid illustrations and simple explanations.
Game theory is a branch of applied mathematics that studies behavior in strategic situations, in which an individual's success in making choices depends on the choices of others, according to www.wikipedia.org.
Fisher creatively introduces the topic with a popular game "Rock, Paper, Scissors." People the world over play different versions of the game. In Japan, it is called "Snake-Frog-Slug" while in Indonesia, it is called "Elephant-Human Being-Earwig."
Whatever the name, the basic rules are the same: rock beats scissors, scissors beat paper and paper beats rock.
The simple game provides useful insights into many problems, Fisher says. For example, the best survival strategy for the worst shooter in a three-way pistol duel is to let the other two shoot at each other first.
This is one case that demonstrates the pervasiveness of the game theory in daily life. "Game theory is all around us. Despite its name, it is not just about games -- it is about the strategies that we use every day in our interactions with other people," Fisher says.
To explain further, he cites the famous Prisoner's Dilemma -- Westerners rarely discuss game theory without mentioning this case. The Prisoner's Dilemma was first thoroughly studied by American mathematician John Nash.
Suppose there are two captured thieves who committed a burglary without leaving behind much evidence.If both thieves plead guilty to burglary and each testifies against the other, both will get four-year sentences. If both thieves plead innocent and refuse to testify against each other, both will get two-years sentences for a lesser crime. If only one of the thieves pleads guilty and testifies against the other, the one who confesses gets three-year sentences while the one who refuses to confess gets five-year sentences.
The best strategy for both thieves is to admit nothing and accuse no one. But as neither thief is sure whether the other would confess, both would consider pleading guilty as a more prudent strategy.
"The Prisoner's Dilemma presents us with a logical conundrum that lies at the heart of many of the world's most serious problems," Fisher observes.
Fisher might not know that more complicated real examples of game theory were abundant in ancient China long before the theory got its name in the West in 1944.
Take the classic example in the Warring States Period (476-221 BC).
Towards the end of that period preceding the Qin Dynasty (221-206 BC), there were six other major states vying for dominance, besides the most powerful Qin State: Yan, Zhao, Qi, Wei, Han and Chu states.
Faced with the threat from Qin, two opposing schools of thought prevailed among the six states: hezong, or alliance with each other to repel Qin's expansionism and lianheng, or alliance with Qin to participate in its ascendancy. While the six states initially were successful in applying hezong, Qin managed to break the alliance by stirring suspicion and jealousy among the six states.
In the end, by repeatedly exploiting the lianheng strategy, Qin managed to defeat the states one by one and thus completed the unification of China.
Both this case and the Prisoner's Dilemma indicate the tendency to egoism at times when there is not enough mutual trust, which often causes damage, not benefits.
An example today are the international disputes over global warming. Worried that taking the lead in limiting the burning of fossil fuels may hinder their economic development, many countries are reluctant to make their due contribution to the reduction of greenhouse gas emissions. Yet if every country takes this approach, the consequences would be disastrous.
Acknowledging this reality, Fisher makes some suggestions about building mutual trust in coalitions. One idea is to make breach of contract costly. Only when the cost of betrayal outweighs its benefits can the efficacy of a binding contract be realized.
But not the entertaining "Rock, Paper, Scissors" by Len Fisher, which elucidates game theory and its wide applications with vivid illustrations and simple explanations.
Game theory is a branch of applied mathematics that studies behavior in strategic situations, in which an individual's success in making choices depends on the choices of others, according to www.wikipedia.org.
Fisher creatively introduces the topic with a popular game "Rock, Paper, Scissors." People the world over play different versions of the game. In Japan, it is called "Snake-Frog-Slug" while in Indonesia, it is called "Elephant-Human Being-Earwig."
Whatever the name, the basic rules are the same: rock beats scissors, scissors beat paper and paper beats rock.
The simple game provides useful insights into many problems, Fisher says. For example, the best survival strategy for the worst shooter in a three-way pistol duel is to let the other two shoot at each other first.
This is one case that demonstrates the pervasiveness of the game theory in daily life. "Game theory is all around us. Despite its name, it is not just about games -- it is about the strategies that we use every day in our interactions with other people," Fisher says.
To explain further, he cites the famous Prisoner's Dilemma -- Westerners rarely discuss game theory without mentioning this case. The Prisoner's Dilemma was first thoroughly studied by American mathematician John Nash.
Suppose there are two captured thieves who committed a burglary without leaving behind much evidence.If both thieves plead guilty to burglary and each testifies against the other, both will get four-year sentences. If both thieves plead innocent and refuse to testify against each other, both will get two-years sentences for a lesser crime. If only one of the thieves pleads guilty and testifies against the other, the one who confesses gets three-year sentences while the one who refuses to confess gets five-year sentences.
The best strategy for both thieves is to admit nothing and accuse no one. But as neither thief is sure whether the other would confess, both would consider pleading guilty as a more prudent strategy.
"The Prisoner's Dilemma presents us with a logical conundrum that lies at the heart of many of the world's most serious problems," Fisher observes.
Fisher might not know that more complicated real examples of game theory were abundant in ancient China long before the theory got its name in the West in 1944.
Take the classic example in the Warring States Period (476-221 BC).
Towards the end of that period preceding the Qin Dynasty (221-206 BC), there were six other major states vying for dominance, besides the most powerful Qin State: Yan, Zhao, Qi, Wei, Han and Chu states.
Faced with the threat from Qin, two opposing schools of thought prevailed among the six states: hezong, or alliance with each other to repel Qin's expansionism and lianheng, or alliance with Qin to participate in its ascendancy. While the six states initially were successful in applying hezong, Qin managed to break the alliance by stirring suspicion and jealousy among the six states.
In the end, by repeatedly exploiting the lianheng strategy, Qin managed to defeat the states one by one and thus completed the unification of China.
Both this case and the Prisoner's Dilemma indicate the tendency to egoism at times when there is not enough mutual trust, which often causes damage, not benefits.
An example today are the international disputes over global warming. Worried that taking the lead in limiting the burning of fossil fuels may hinder their economic development, many countries are reluctant to make their due contribution to the reduction of greenhouse gas emissions. Yet if every country takes this approach, the consequences would be disastrous.
Acknowledging this reality, Fisher makes some suggestions about building mutual trust in coalitions. One idea is to make breach of contract costly. Only when the cost of betrayal outweighs its benefits can the efficacy of a binding contract be realized.
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