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What is Game Theory?

TNN Apr 21, 2003, 01.29am IST

In the broadest terms, game theory analyses how groups of people interact in social and economic

situations. An accurate description of game theory is the term used by psychologists the theory of

social situations.

There are two main branches of game theory: co-operative and non-co-operative game theory. Most ofthe research in game theory is in the field of non-co-operative games, which analyses how intelligent

(or rational) people interact with others in order to achieve their own goals. It is called 'game theory'

because it models individual behaviour as if two or more people were participating in a game, at the

end of which either player gets a payoff (or some benefit). Thus, the game itself evolves as each playermoves, or uses the strategies available to him, in order to achieve the best outcome (or the highest

payoff) for himself.

Who is regarded as the father of modern Game Theory?

Contrary to popular perception, the father of modern game theory is not John Nash, though he did

make seminal contributions to this field. Mathematical game theory was invented by John von

Neumann and Oskar Morgenstern in 1944. John Nash extended and generalised the pioneering resultsachieved by von Neumann and Morgenstern, for which he won the Nobel Prize for Economics in 1994.

He is best known by the 'Nash Equilibrium', a situation that can be described as the stable outcome

resulting from two or more players adopting strategies that they think will maximise their individual

gains from a situation or 'game'.

Are game theoretics only this recent?

Although the systematic mathematical form of game theory is owed to these two, game theoretic

insights are far older than that. For example, Plato, in the Republic, at one point has Socrates worry

about the following situation. Consider a soldier at the front, waiting with his comrades to repulse anenemy attack. It may occur to him that if the defence is likely to be successful, then it isn't very

probable that his own personal contribution will be essential. But if he stays, he runs the risk of being

killed or wounded apparently for no point. If the enemy is going to win the battle, then his chances

of death or injury are higher still, and now quite clearly to no point, since the line will be overwhelmedanyway.

Based on this reasoning, it would appear that the soldier is better off running away regardless of who is

going to win the battle. Of course, if all of the soldiers reason this way as they all apparently should,

since they're all in identical situations then this will certainly bring about the outcome in which thebattle is lost. So what does a commander do to prevent this rout? He changes the incentives of his

soldiers by shooting all deserters, discouraging mass desertion before a shot has been fired.

What are the economic applications of Game Theory?

The work of von Neumann and Morgenstern led to the application of game theory in economics. Manyeconomic situations are situations where players have to act competitively, or bargain, to achieve the

best result for themselves. One example is the bidding for spectrum by cellular operators. The auctions

are designed using game theory so that the highest bidder gets bandwidth without paying too much

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(avoiding the 'winner's curse').

Some extensions of game theory try to capture the distribution of resources between various competing

uses as a bargaining problem. This can be at the macro level as to how governments spend money

between various competing uses, and at the micro level as to how households divide resources betweenvarious members, say between men and women.

Are there non-economic applications as well?

One of the best known applications of game theory was in the field of political science: the

understanding of Mutually Assured Destruction (MAD) in the event of nuclear war , and the nature of

the arms race. In the case of MAD, a game would capture how the best strategy for two nuclear powerswith equally effective destructive capacity is to not launch a missile, failing which disaster would ensue

for both parties. Therefore, the best, or 'dominant' strategy for either player is to not launch a missile.

The arms race example has the opposite effect. If two countries are faced with the choice of eitherspending money on welfare or on buying weapons, then both would end up spending on arms, because

each would fear that the other will arm itself, and neither would want to be defenseless against the

other. As a result, while the socially preferable outcome would be to spend on welfare, the socially

inferior outcome (increased arms expenditure) obtains instead.