# Game Theory

Game theory is the term given to the methodology of using mathematical tools to model and analyze situations where decision-making is interactive, usually called ”strategic”. Hence, it is concerned with the choice of decision-makers, usually called ”players”, with different goals, where the decisions of each decision-maker may have an impact on the outcome for all decision-makers. This interactive nature distinguishes game theory from classical decision theory where a single decision-maker has to make a choice facing a ”passive” environment. Game theory aims to clarify the structure of interactive decision-making situations, to predict the behavior of decision-makers and to give advice to decision-makers in such situations. Since the fact that game theory is a theory that can be characterized as a context-free mathematical toolbox, it can be applied in any situation of interactive decision-making.

The foundations of modern game theory go back to the book ”The Theory of Games and Economic Behavior”, published in 1944 by the mathematician John von Neumann and the economist Oskar Morgenstern. Since then the theory has been developed extensively. Today has applications in a wide range of fields such as economic theory, network theory, political science, military, law, computer science, biology, sociology, anthropology, psychology, and philosophy.

From a methodological point of view game theory is inherently tied to mathematics as the game theory makes use of a variety of mathematical tools. The analysis of some game-theoretic models even required the development of new mathematical tools.

The field of game theory can be divided into three board sub-fields: non-cooperative game theory, dealing with so-called strategic games, which assume the non-existence of binding agreements, cooperative game theory dealing with so-called bargaining games, which allow for binding agreements, and evolutionary game theory. The non-cooperative game theory is basically concerned with decision-makers acting independently from each other and with each decision-maker trying to achieve its most desirable outcome. This also holds for cooperative game theory, but with the already mentioned difference that it is assumed that decision-makers can sign binding agreements, i.e., agreement, which are enforceable. However, in many cases, interactive decision-making problems requires a modeling, which makes use of both sub-fields of game theory. Finally, evolutionary game theory, which is a newer sub-flied of game theory, which has its origins in biology. It deals with the development of populations. It defines a framework of contests, strategies, and analytics into which Darwinian competition can be modeled. The evolutionary game theory differs from the other two sub-fields, known as ”classical game theory”, in focusing more on the dynamics of strategy change. However, it also found its way to other applications such as the development of technical norms and standards.

Today, game theory as an important tool in many fields is widely recognized. Since 1994 eleven game-theorists won the Nobel Memorial Prize in Economic Sciences: John Forbes Nash Jr., John Harsanyi, Reinhard Selten, William Vickrey, Robert Aumann, Thomas Schelling Alvin Roth, Lloyd S. Shapley, Eric S. Maskin, Roger B. Myerson, and Jean Tirole. Moreover, John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology. In the past, some of these have attended the SING meetings.