The Incredible game theorist

Mr. Nash's work needed refining. First, it applies to games played only once, or in which players move simultaneously. But virtually all interesting economic games involve continual interaction between players. Mr. Selten extended the Nash equilibrium to these settings. From that emerges the importance of credibility: there is no point in one player following a plan which other players know will have to be changed at some point.

For example, a monopolist might try to keep a would-be rival out of its market by threatening a price war if the rival steps in. Such a war may mean that the entrant would make a failure. But it would be costly for the monopolist, too. If the price war costs a lot, the monopolist would do better to share the market with the new entrant. In that situation, the threat of a price war is not credible: the entrant can go into the market, knowing the incumbent would be foolish to fight back.

Second, it is not realistic to assume that players know what is in each other's minds. As Adam Brandenburger of Harvard Business School puts it, "games are played in a fog," Mr. Harsanyi cut through the mist, by showing that games in which players are not well informed about each other can be analyzed in almost the same way as ordinary games.

When some players have information that others do not, their strategies can alter their reputations to their advantage. A government that shoves interest rates up to signal its anti-inflation credentials is one example.  Bond traders do not know whether it truly wants to curb inflation, but hope that it might; the longer interest rates stay up, the more hopeful they get. Or take a monopolist that would like to stop entry into its market. It can do so if would-be rivals fear that it likes fighting price wars, in spite of the cost. By fighting anyone who does enter, the monopolist can build a reputation as a price warrior and put other entrants off.  An oligopolist may be able to keep profits up by setting high prices and nurturing reputations for being friendly to their rivals.

Yet some economists are still cautious of game theory, in spite of the insights it has brought. That is partly because the theory is difficult: it demands lots of difficult mathematics. That, however, is merely a reflection of the complexity of the world. But there is a more telling objection—namely, that game theory is just that: theory. So far there have been valuable few real-life applications. Game theorists have been good at describing the intricacies underlying strategic interdependence and generating ever more refined concepts of equilibrium, though less adept at providing governments and firms practical advice.

Even that criticism, however, is weakening. Central bankers now know (or should know) all about reputation and credibility. America's Federal Communications Commission used game theorists to design 1994 auction of radio spectrum. And businesses, too, are beginning to learn about game theory: Harvard's Mr. Brandenburger, for illustration, teaches it to MBA students and executives. The time is coming, he says, when self-respecting MBA’S, as well as economics graduates with a taste for math, will not leave school without it.