<B>The potential of Game Theory</B>

Juan Santaló. Professor. Instituto de Empresa

9 January 2006

This year, two scientists were awarded the Noble Prize for their work on Game Theory. While one laureate applied the theory to formal mathematical construction as a way to understand objective probability, the other used the theory to analyze international relations and human interactions. Obviously, Game Theory shows enormous potential for anticipating the outcome of a wide range of situations.

This year's Nobel Prize was awarded to two eminent economists who have worked on so-called Game Theory. This discipline has a wide range of uses, including the ability to study and analyze the decisions made in situations, ranging from the well-known children's game of Rochambeau (scissors, paper, rock) and the regattas of the America's Cup to the Cuban missile crisis and the war between Canal Satélite Digital and Vía Digital for the pay-per-view TV market.

But what is the common denominator that makes it possible to analyse all these situations using Game Theory? In each case, the outcome depends on the decisions made or the strategies adopted by each of the different participants or players. In this way, the advantage or the loss of each player depends not only on his/her own strategy, but also on the strategy of the other players. Accordingly, Game Theory is useful for analyzing situations in which different participants interact and in which each attempts to predict the strategies of the others.

Aumann and Schelling, the two award-winning scientists, have looked at the potential of Game Theory for analyzing and understanding a broad range of social and economic phenomena. However, each laureate has focused his research on a different aspect of the theory. Aumann contributed to the formal-mathematical construction of the theory by carefully differentiating between games with an infinite duration and games with a specific duration. He also formalized the concept of subjective probability, which is of key importance for making uncertain decisions.

For his part, in the subtitle of one of his books, Thomas Schelling has defined himself as a 'wandering economist'. This label is not the result of a long journey around a great number of academic centres throughout the world. Indeed, Schelling has spent most of his career at Harvard, where he made his most significant contributions to science. Nonetheless, since 1990 he has been a professor at the University of Maryland.

The label of 'wandering' is due to the continuous journey of his lucid thought through the different realms of social phenomena. In fact, this economist has used his capacity for analysis to study international relations. His book Strategy of Conflict has become a classic and has had great influence on political science, sociology and other fields. In other brilliant contributions to science, he has analysed racial segregation and studied the way in which individuals struggle to control their own behaviour.

One example given by Schelling may shed light on how his hypotheses can have a variety of applications. Imagine that for some strange reason you need to meet up with a person you don't know in Madrid on a certain day at a certain time. You and this person know absolutely nothing about each other except that you both have the same urgent need to meet. To make it more difficult, you have no way of communicating with each other. You both simply have to guess where you need to be in order to coincide.

Where would you go when the moment came? The most common answer when this game is played, is somewhere in the central plaza of la Puerta del Sol—most likely, the statue of the Bear and the Strawberry Tree.

In class, I ask my Instituto de Empresa students the same question, adding the fact that the two unknown people are students at this business school. The most common answer in this case is the school entrance. For Schelling, La Puerta del Sol and the entrance to the Instituto de Empresa are examples of focal points that come to mind naturally when everyone stands to gain and if participants are co-ordinated but communication is impossible or, at best, extremely difficult.

These concepts are immediately applicable when companies are setting prices or simultaneously adopting new technologies. Another of Schelling's great contributions has been the ability to identify the conditions for determining when a threat or promise is credible and when it can be considered a bluff. In short, the work of Aumann and Schelling has laid the groundwork for understanding a wide-range of economic and social phenomena. And I offer them my most humble congratulations!

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