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It sounds pretty obvious: life is all a game. Charles Lamb $(1775-1834)$ put it rather elegantly: “Man is a gaming animal. He must always be trying to get the better in something or other.” What John Harsanyi and other economists did was to apply mathematical Logic to this human urge and make game theory, as it is called, part of the ir tool kit. At its humblest level, game theory is useful in saving the players from going mad. In devising a strategy you know that your rival may know what you are planning, and he knows that you know he knows, and soon.... even skilled chessplayers can feel mentally wounded.

In chess and comparable real-life games, each side has basic information about the other. The problem of Charles Lamb’s gaming animals is that they usually have imperfect knowledge about their opponents. They guessed, or relied on “intuition” or, as Napoleon said of his favorite generals, they were lucky. Until quite recent items, this was the way countries and great companies dealt with their rivals.

Mr. Harsanyi’s contribution to game theory was to show that such games need not be played in a fog, or at least not much. It was possible to analyze such games and provide guidance about the probable moves and their outcomes. This advanced game theory was employed, at least by the Americans, in their negotiations with the Soviet Union on arms control. Kennedy and Khrushchev used game theory in their tussle over Cuban missiles in $1962.$

Game theory is widely used in commerce, as happened this year when, with great success, the British government sold licenses for mobile phone services in an auction designed by an Oxford economist. Paul Kemmerer. Some economists are watching with fascination the contest between the European Central Bank and the currency market over the future of the Europe, which has at least the look of an exercise in game theory. A Dutch team of economists applied the theory to international football and concluded that a bad team playing at home is more likely to score than a good one playing away. One effect of game theory is to make economists seem quite human.

As often happens when an idea becomes fashionable, there has been some argument about who first thought to game theory. Mr. Harsanyi, who shared a Nobel Prize in $1994$ with two other economists in the same field, John Nash and Reinhardt Selten, was happy to acknowledge that game theory had been around in some form for a longtime. Players of poker, and of course chess, had been using game theory without calling it that. Philosophy has a claim: it seeks to rationalize the behaviour of people with conflicting interests. As a young man in Budapest, Mr. Harsanyi had studied philosophy and mathematics and, to please his parents who ran a pharmacy, he added chemistry.

What triggered his interest in game theory appears to have been the work of John von Neumann and Oskar Morgenstern, who in $1944$ published a book entitled “The Theory of Games and Economic Behaviour”. Von Neumann was an American mathematician who, by coincidence, had also been born in Hungary and had attended the same school as Mr. Harsanyi. He and Morgenstern may have been the first to show how the philosophical idea of rational behaviour could be applied to economics. They did not develop the idea. In his short life, von Neumann especially had much other interest, including work on quantum theory and the design of the first electronic computers. In paper after paper, Mr. Harsanyi and his colleagues took the theory further. It is still being polished.

The philosopher in John Harsanyi saw in game theory means of improving the human condition. He promoted the idea that the rightness or wrongness of an action depended on its consequences. An ethical theory known as utilitarianism. The connection between game theory and ethics is a complex one. His book on this theme, Essays on Ethics. Social Behaviour and Scientific Explanation”, is a hard read, just as game theory it self demands lots of tricky mathematics. No one would blame you for sticking to Charles Lamb.

What is the author meaning to convey when he says, “even skilled chess-players can feel mentally wounded”?

1. it saves the players from going mad
2. the mathematical logic of the game theory leaves even skilled players wounded
3. that the theory is very complicated
4. chess players find the theory hard to comprehend

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