John Nash, Jr., whose life was depicted in the book and Academy Award-winning film A Beautiful Mind, was killed in a car accident along with his wife on May 24. They had just returned from Norway, where Nash was awarded the prestigious Abel Prize for his contributions to the field of partial differential equations. Nash is best known for his contributions to game theory — the study of interaction and decision-making strategies between different rational actors. Nash's work, particularly the Nash Equilibrium, have given rise to foundational concepts in this field. Although Nash was a mathematician at heart, his work in game theory has had far-reaching implications that span well beyond the field of quantitative theories, changing the way we understand human psychology, global trade and even strategic forecasting.

At the core of Stratfor's worldview is our geopolitical framework for looking at at the constraints and consequences of the actions of world leaders, global businesses and other actors. The limitations placed upon these different actors vary greatly. Whether it be the military constraints facing Ukraine or the geological constraints facing Japan, these variables limit the number of actions a state actor can take. By employing Nash's work in game theory, we can better analyze and understand the framework within which global leaders and states will act, react and make future decisions.

Nuclear Deterrence and Game Theory's Utility

Game theory emerged from collaboration between an economist and a mathematician. From the start, many of its most important applications have been in strategic and tactical military thinking. John Nash's Nash Equilibrium describes an outcome in which an actor cannot deviate from his or her own strategy to achieve a more advantageous outcome. Essentially, the equilibrium is an actor's best response to the strategy of every other actor.

Although the concept of such an outcome is seemingly obvious, Nash's formulation of the equilibrium directly shaped the U.S. and Soviet Cold War strategies. With both countries in a nuclear standoff throughout this period, Henry Kissinger, Robert McNamara and other leaders used Nash's concept to justify their decision not to launch an initial nuclear strike because this action would be followed by a retaliatory strike that assured mutual destruction. Deviation from the initial strategy of nonaggression would be negative for both opponents.

When articulated in these terms, Nash's line of thought appears rather simple. When applied to most real-world situations, however, game theory as well as its optimal strategies and payoffs depend on how an analyst translates the complexity of reality into the strict rules and confines of a "game."

In order to examine this complexity, it helps to look at a simplified version of the Cold War nuclear threat game. Let us assume that at the start of each day the leader of either country can decide to attack or not to attack. If one leader decides to attack, the other leader must then decide whether to retaliate.

As formulated above, the only outcome where neither leader can change his strategy to obtain a better payoff (the Nash Equilibrium) would be if neither country strikes first. If one side starts a nuclear conflict and the second retaliates, the initiator of conflict would be better off having never fired the first shot. Even if there is no retaliation, the initial attacker could not guarantee that it had destroyed the enemy's entire nuclear arsenal, leaving itself more exposed to a retaliatory strike. For the opponent hit first by a nuclear attack, however, not retaliating would set a dangerous precedent for their response to potential future nuclear attacks.

When the rules and terms are set in this way, it is easy to understand why an initial nuclear attack would never be the most advantageous decision for either side. But this outcome is largely a construct of the way this version of the game was put together. An alternative set of rules would follow the classic "prisoner's dilemma," in which both sides must make the decision to attack or not attack without knowing what the other side will do in addition to how the other side will react. In this version of the nuclear game, the dominant strategy for both sides would actually be to default to a nuclear attack. Regardless of what the other actor decides, both sides are better off attacking. The Nash Equilibrium here is a strategy of aggression.

For world leaders, this decision-making scenario is replayed endlessly — every day, every hour and every minute. When this repetition is factored in, empirical evidence suggests that one of the best courses of action follows a "tit-for-tat" strategy. In it, after each time the game plays out an actor should simply copy what the other side did the previous round. This strategy has its own issues in application, but with each additional complexity the theorems and conditions that come with the scenario change as well.

Another complication in this scenario is that payoffs in nuclear deterrence or strategic thinking are often open to interpretation. If circumstances surrounding both sides change, then the payoffs would change accordingly and the opposing strategies would as well. An example of such a situation would be if either the Soviet Union or United States faced an existential threat to which the only response was nuclear.

Despite these limitations, game theory provides a framework, just as geopolitics does, to evaluate the potential strategies and outcomes of various political "games," such as the use of nuclear weapons. If nothing else, it is a valuable tool to analyze questions and properly identify the constraints, actions and possible strategies actors will take and, most important, how actors will react when the underlying circumstances change.

OPEC and Production

In addition to outlining possible nuclear disasters, Nash's work has also impacted how the world understands and reacts to economic disasters. Following the collapse of global oil prices in June 2014, business leaders and energy producing states have tried to gauge Saudi Arabia's strategic thinking on oil prices and production levels. In the past — and as recently as 2008 — the Saudis had often maintained high global prices by organizing an OPEC production cut.

However, Saudi Arabia's recent policy has been the exact opposite. Instead of restricting its own output, Saudi Arabia has increased exports to their highest levels since 2005, exporting almost 7.9 million barrels per day of oil. The reason for Saudi Arabia's new strategy is no secret: the circumstances changed.

The oil price drop at the end of the first decade of the 21st century was largely a result of shrinking global demand following the worldwide financial crisis. In this economic environment, if Saudi Arabia and OPEC had decided to cut their production to raise prices, there would be no immediate response by any other producers. Most oil production outside of OPEC had stagnant or declining growth, and producers would be unable to fill the hole left by OPEC's shortages. In a sense, if OPEC could raise the price of oil through reduced exports, no other oil producer had the ability to respond, thus making it a desirable strategy for Saudi Arabia.

The recent price collapse, however, was different. It occurred not because of a drop-off in demand, but because of a glut in oil production stemming largely from the introduction of North American shale oil. In this new energy landscape, other oil producers would be able to respond to a cut in Saudi production by producing more. In short, Saudi Arabia would only hurt itself by deviating from its current output strategy. By cutting production and keeping prices relatively high, Saudi Arabia and OPEC would only re-incentivize North America and other emerging oil producers to invest in new production capabilities. Although it is a weak strategy on the part of the Saudis, there is little reason to think that they will deviate from it until there is a structural shift in the game.

Some oil analysts have suggested that Saudi Arabia could pursue another strategy: cut production and forfeit some market share to help maintain stability in Arab states whose budgets are tied to high oil prices. Following that line of thinking, Saudi strategy rises to a higher level less rooted in purely economic calculations. Stratfor's argument, however, rejects this, contending that Saudi Arabia's actual concerns for other OPEC members are relatively limited. Looking along the immediate Saudi periphery one finds countries that are either financially well off regardless of the relatively low oil prices (Kuwait, Oman, the United Arab Emirates and Qatar) or are net energy importers (Egypt, Jordan and Israel) that benefit from low prices. The lone exception is Yemen, which has its own host of issues not related to the price of oil.

Greece, Europe, the IMF and Head-On Collisions

Another case study that benefits from the application of game theory is the debate between the Greek government, the European Commission, the International Monetary Fund and the European Central Bank. Athens' calculations undoubtedly factor in game theory because the Syriza party's finance minister, Yanis Varoufakis, is an economist. Varoufakis wrote his dissertation on game theory and has produced several books on the subject, exploring its application to political economy.

One way to look at this game is through the lens of what is known as the "chicken game." In this game, two drivers are driving quickly directly at one another, each waiting for the other to blink and swerve off course. If the two crash, both drivers die — clearly a poor outcome. If only one driver swerves, the driver who did not swerve proves his resolve and has his most desired outcome. If both drivers swerve, this is better than being the only one that swerved, but not as good as sticking it out and "winning."

In this game, there are two Nash Equilibriums in both permutations of one player swerving and the other maintaining course. In either scenario, the driver who did not swerve would be worse off if he swerved whereas the one who swerved would be dead if he did not. However, the difference between the chicken game and the prisoner's dilemma (where either player's optimal strategy is to always go against the other) is that in the chicken game, neither always swerving nor always not swerving is an optimal strategy.

As Greece negotiates its bailout package with lenders and European leaders, both sides have entered a chicken game and neither has been willing to change its course of action. The European Commission, the International Monetary Fund and the European Central Bank are all attempting to preserve the status quo, maintaining the reformist program imposed upon Greece, which they believe will ultimately lead to a repayment of their loans. The Greek government is trying to avoid the reforms, believing that the debt and reforms together are choking its economy. Athens instead believes debt forgiveness would be a more productive solution.

In a sense, both sides have driven along the road toward one another and, now, if neither swerves, the collision — a Greek exit from the eurozone — will be the outcome. Ultimately, however, the most likely scenario is that the two sides will defer from their optimal option and reach an accommodation. In both the chicken game and the prisoner's dilemma, neither side is able to communicate or negotiate with the other. A key difference in the European talks is that both sides can gauge and react to the other's stance.

Varoufakis and the Greeks are banking on the prospect that a Greek exit from the European Union would set a politically dangerous precedent for the organization — one that Brussels needs to avoid. By challenging, and potentially changing, the perception of the eurozone monetary union, Greece's exit could suddenly change the conglomerate into nothing more than a set of exchange rate mechanisms that countries could leave at will, undermining market confidence in the euro. Varoufakis is betting that Europe's economic leaders will avoid this outcome at all costs and eventually compromise with Greece. In terms of the game, Athens thinks Brussels will swerve. Greece just played this game in February, when it negotiated an extension with the International Monetary Fund, European Central Bank and European Commission. 

Opposite the Greek stance, German Minister of Finance Wolfgang Schauble has made the argument that a Greek exit from the eurozone is not all that bad for Europe and that the option is still on the table. German Chancellor Angela Merkel, who is perhaps more concerned about the prospect of Greece being pushed toward greater Russian influence if it is kicked out of the eurozone, and the potential ramifications for Ireland, Spain and Italy, will likely swoop in to ensure that a deal is made.

This difference in German opinions underlines one of the core difficulties of applying game theory to real-world events: understanding whether there is knowledge of the other player's payoffs. Both Schauble and Merkel are presenting drastically different tolerances for the prospect of a Greek exit and the extent of needed reforms. It makes it more difficult for Athens to assess the true position of Berlin and its willingness to cave in to weaker constraints on reforms.

While John Nash, Jr., was far from the inventor of game theory, his impact on the field has been far-reaching. He formalized the distinction between cooperative games and non-cooperative games. While the examples discussed here largely fall under non-cooperative games, coalition forming in entities like NATO or the eurozone often fall under the former.

Both geopolitics and game theory rely on the belief that countries and decision-makers, particularly leaders who would not have gained their position if they were inept, are rational actors reacting to their own constraints. Game theory, like geopolitics, discounts the role of personality in forecasting an outcome, instead contending that a rational actor will follow the rules of the game or react to geopolitical constraints. Defining those constraints then comes down to defining this game. Of course, the challenge is fitting a real world decision-making process into an axiomatic system to define the game. Such a process is never fully accurate, and it is nearly impossible to account for every variable at play. Nevertheless, Nash's work has provided us with a sounder, more cogent method of understanding the facets of global events. 

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