= GAMES OF DETERRENCE AND THE BREAKDOWN OF CLASSIC GAME THEORY =
Classic game theory lends itself very well to the analysis of "zero-sum games" where any gain by one or more players must be equal to the loss of one or more rivals. Such a game recalls Machiavelli's observation: "The Prince who promotes another's power diminishes his own." This concept is particularly convenient for the analysis of situations of merciless interest antagonism in two-person games, such as duels; and several early applications of game theory have dealt with calculations of the best time at which each of two mutually approaching duelists—or of two mutually approaching fighter planes—should open fire, in order to use his limited ammunition to best effect. Such analyses of duels are useful not only for improving certain tactics of aerial combat. In a world whose international politics seem characterized at least temporarily by a "bipolar power system," it seems plausible to apply the same style of thinking to duels between individuals and to power conflicts between rival blocs, or between the two nuclear-armed superpowers who appear to lead them.
A more refined approach, then, consists in treating the two-person game as a mixed-interest game, in which both countries have not only antagonistic interests but also significant interests in common. This area of mixed-interest-games has been explored by a number of writers, and most notably by Thomas C. Schelling.
Schelling uses game theory not so much in a technical sense, as a professional practitioner of this subject might do, but as a source of ideas and suggestions that he develops in his own way, perhaps with fruitful effects for the discussion among game theorists themselves. His book The Strategy of Conflict represents an unfinished but important intellectual contribution. At times it reads like the notebook of a creative social scientist, communicating the excitement of new insights and discoveries.
In eminently lucid and often charming language, Schelling's work opens to rational analysis the international politics of threat deterrence. In this field, his analysis goes well beyond what has been done by earlier writers. At the time of its appearance it was the best, most incisive, and most stimulating work on the subject, and will rank among the top contributions for a long time to come.
Threats, Schelling suggests, are meaningful only among persons or countries that simultaneously have important interests in common. A fruitful mathematical model for such situations is offered by "mixed-interest games," rather than by the "zero-sum games" of pure hostility and completely opposite interests—on which too much attention of the popular writers on game theory has been concentrated.
The logical opposite of these zero-sum games are the pure coordination games that occur between players whose interests coincide completely but who must coordinate their moves in the face of incomplete information, the pressure of time, or other handicaps. Thus, even if the United States and Russia had none but common interests in preventing third countries from acquiring nuclear weapons, they would be faced with a game problem in coordinating their policies in the face of mutual ignorance, and before other countries—such as, say, China, Japan, or Germany—would enter the ranks of the atomic powers. Since the United States and Soviet Russia also have important interests that clash, their mutual foreign policy problem resembles a "mixed-motive game"; and it provides, according to Schelling, a suitable field for the use of both promises and threats as instruments of policy.
Threats are effective, according to Schelling, in proportion to their intensity and credibility. Since nuclear weapons have made it easy to increase greatly the intensity of war among great powers, the crucial problem that emerges is that of making such threats credible—since their execution normally would involve also some serious damage to the threatening party.
