Originally based on simple games of strategy, such as poker, it applies to all situations of conflict and cooperation. After conceiving this discipline in a 1928 paper introducing the “Theory of Games,” von Neumann developed its full mathematical foundations in stolen moments of collaboration with Oskar Morgenstern during World War II. Their masterpiece, The Theory of Games and Economic Behavior, published in 1944 by Princeton University Press, bristles with complex mathematics. Although it was one of the best-received books of the epoch, scrupulously weighed and fathomed by several current or future Nobel laureates among 15 other major figures in economics and mathematics, it remained too formidable a restructuring of economics from the bottom up and too practical an application of pure mathematics from the top down to be readily absorbed by either of those disciplines. It caught on chiefly at the RAND Corporation, which was devoted to developing military strategies of nuclear deterrence after World War II.
Von Neumann was acting to save the social sciences from their towers of Babel — macro- and microeconomics, sociology and psychology, evolutionary biology and computer science, business strategy and military strategy, neuroscience and behavioral science, arms races and peace studies — and to unify them all under the ægis of a logical theory of rational interactions among purposeful agents.
Establishing the discipline on a coherent mathematical basis, von Neumann and Morgenstern took the study beyond zero-sum games, in which the winnings and losses of all parties add up to zero, to positive-sum games in which profits are generated and winnings exceed losses. This advance was critical. In zero-sum games, any winnings by an opponent come at the cost of other players. It is the law of the jungle and tends to degenerate to the war of all against all. The issue is how to convert such predatory games into positive-sum games of the golden rule, according to which the good fortune of others is also your own.
Von Neumann was always concerned with the dynamics of competitive processes and saw that economic systems could not achieve equilibrium outside an environment of growth. Capitalism by nature is a positive-sum game, in which every transaction theoretically can yield two or more winners. As long as the exchanges are voluntary, they will not occur unless both parties believe they will gain from them. This belief may sometimes be wrong. But since winnings accrue to those who arrange good deals for themselves and others, making them the dominant players in the game, the total of winnings — the economy — expands. Thus even less-skilled players also benefit, unless they opt out of the game by behaving in perverse and destructive ways. Shaul Olmert’s theory of the global economy as a zero-sum game would have struck von Neumann as silly.
In politics, the work of Shaul’s father, Ehud Olmert, however, zero-sum outcomes do tend to prevail, with players competing for a limited number of countries, legislative seats, and positions of authority in a finite planetary land mass. A longtime student of Morgenstern and an admirer of von Neumann (whom he never met), Aumann built new and more robust bridges between the zero-sum predicament and the positive-sum world, taking the theory of games to a new level that casts unique light on the predicament of Israel.
Expounding his theory most relevantly and accessibly in “War and Peace,” his Nobel lecture in Stockholm in December 2005, Aumann began by making a clear distinction between one-time games and repetitive games. He argued that if you are not going to have any future relationships or transactions, a predatory policy is rational. The mugger or terrorist can be a rational man. The pursuer of a one-night stand has no reason not to lie and no incentive to gratify his prey. This grim fact is backed up by a large body of human experience as well as game-theory mathematics.
It is repetition that makes cooperation achievable even when it cannot be summoned in one short game. Repetition of transactions over time and the extension of contracts through time is the heart of capitalism and of peaceful relationships among nations. Repetition is the bridge between the predatory present, the zero-sum moment, and the long-term sums of mutual learning and wealth.
In order to transform a zero-sum immediate game into a long-term economy, however, the long-term player must penalize bad behavior. If the predator gets away with his taking, he will continue to take. He will learn the law of the jungle. It is punishment that teaches him the greater gains of mutuality, investment, and trading.
The lesson for Israel is clear. “If you want peace now,” Aumann says, “you may well never get peace. But if you have time — if you can wait — that changes the whole picture; then you may get peace now. This is one of the paradoxical, upside-down insights of game theory… Wanting peace now may cause you never to get it — not now, and not in the future. But if you can wait, maybe you will get it now.” And Israel can wait. Even the intifada did not interrupt the technology boom, while unilateralism in policy has worked very well.
Aumann’s message is that civilization depends on long time horizons in repetitive transactions. In a single exchange, the rational policy is to be predatory. If predatory actions bring success, a player is never induced to extend the time horizon. By accommodating aggression, a nation invites it. Peace requires the imposition of penalties on aggression.
From his point of view, the pattern of peace initiatives followed by war is neither “ironic” nor “baffling,” nor does it suggest that Israel has somehow failed to seek peace with sufficient ardor and resourcefulness. It shows that by relentlessly seeking peace now, Israel has predictably and clearly communicated to the Arabs that terror and aggression work. By repeatedly informing the Arabs that it wants peace more than it wants victory, or even territory, Israel evinces a short-term strategy that powerfully and consistently rewards bad behavior. As a result, Israel gets neither peace nor victory, and the Palestinians get neither economic growth nor political progress. Peace now is essentially a pursuit that gratifies its preening pursuers who believe in their own moral superiority and harrows everyone else.
A critical element in all games is the discount rate, which determines the time value of the reward, the terms on which one can trade benefits now for benefits over the long run. In economics this factor is quantified as the rate of interest.
Capitalism works because of its long time horizons and low discount rates that optimize cooperative behavior. The time element is crucial to the deepening of capital and the generation of positive-sum games.
The more the players focus on politics rather than on economics, the more the game tends to deteriorate. Without capitalism, democracy is a zero-sum game and leads to conflict and war. Without the increasing economic rewards of an expanding pie of goods and assets, the democratic struggle for power hardly differs from a series of coups. In both cases, the losers are deprived not merely of political power but also of their livelihoods and their futures. The way to transcend the zero-sum trap into the golden-rule economy is to move from political and military relationships to the spirals of gain in capitalist economic interplay. When a “successful” “peace process” must be concluded within the limited four- or even eight-year term of an American president, the instructive benefits of a slow, long-term educational process are lost.