The definition of Game Theory can be given as a branch of applied mathematics that focuses on the search for an optimal strategy to achieve success in the presence of competition, uncertainty and lack of information. Therefore, it is the field where decision-making and modeling in competition and conflict situations seen in all sectors and disciplines correspond in mathematics.
Life is about survival and survival means competition. When multiple parties are confronted with a “win or lose” scenario and under constraints such as lack of resources, competition will arise between the parties. The word “parties” here refers to individuals, organizations or states. When it comes to human beings, inevitable and natural competition is present in all these human-created ecosystems.
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Countries fighting for land, businesses competing for market share, animals fighting for natural resources and political parties competing for votes… In dynamic systems and in a world governed by agents who aim to maximize their “value”, Game Theory manifests itself in every field.
Although the related academic field was officially established as “Game Theory” only in the 1950s, similar ideas and behaviors to Game Theory can be found throughout human history. Below, we will first list the works written in the past centuries that gave the green light to Game Theory. Then we will take a look at the rise of Game Theory in every field since its inception in the 1950s.
History
Looking back, we see that the ideas underlying Game Theory have been germinating throughout history. From Sun Tzu’s thoughts on warfare to Charles Darwin’s evolutionary discoveries, Game Theory has existed for centuries as a driver of human behavior. However, the historical foundation of Game Theory is often traced back to the following three specific works. These are: “Researches on the Mathematical Principles of the Theory of Wealth” by Augustin Cournot, “Mathematical Psychics” by Francis Ysidro Edgeworth and “Algebre et calcul des probabilites” by Emile Borel.
These classics shed light on the future of Game Theory and each of them reflected the most advanced mathematics of their time. However, as mentioned above, all these works are only harbingers of the birth of the original discipline. For this very popular field of today was not officially recognized until the 1950s.
Mad Brains: Neumann and Nash
Although almost all of the contributors have a place in the history of Game Theory, the modern analysis of the field began with John von Neumann. Subsequently, it is widely recognized that its methodological framework was established by a well-known name, John Nash.
Until John von Neumann first published his paper “On the Theory of Games of Strategy” in 1928, the field was probably not even called “Game Theory”. To understand the importance of the paper, it is enough to review the fundamental theorem of Game Theory as defined in the paper.
The fundamental theorem of Game Theory applies broadly, that is, to two-person games, including not only individuals but also organizations and states. According to this theorem, it is always possible to find an equilibrium point in a two-person game from which no player should unilaterally deviate. Such an equilibrium exists in any two-person game that satisfies the following criteria. The criteria are:
-The game is “finite”, i.e. it ends in a finite number of moves,
-The game is “complete information”, i.e. the players in the game know their personal strategies and outcomes as well as the other players, and in addition, each player knows that the other players also have complete information,
and finally
-The game is a “zero-sum game”, meaning that one player’s gain is equal to the other player’s loss
as the Minimax Theorem.
This theorem, now known as the “Minimax Theorem”, is very basic and simple, but still very valid. However, following this work, Neumann’s second paper below was, and for many still is, the holy scripture of Game Theory.
“Theory of Games and Economic Behavior”, published in 1944 by John von Neumann and economist Oskar Morgenstern, is considered a seminal text in mathematics, formally establishing Game Theory as an interdisciplinary field of research.
The second major contributor is none other than John Nash, aka “A Beautiful Mind”. Nobel Prize-winning mathematician John Nash’s fame in the field of Game Theory comes from his extension of Neumann’s previously defined two-player game equilibrium. This equilibrium point, known as “Nash equilibrium”, applies not only to two-player zero-sum games, but also to other games. More generally, Nash proved that in a non-zero-sum finite game with n players, each player has an optimal strategy. This is such a generalization that, thanks to Nash, game theory has become adaptable to all areas of competition in our daily lives, from finance to politics, from sports to trade.
Rising on the shoulders of Neumann and Nash, game theory has spread to all sectors and academic disciplines without any borders over the years. Game Theory, which we first saw its initial applications in philosophy and political science in the first half of the 1950s, is at the peak of its attractiveness and impressiveness today, 70 years after those years. For further information, it may be pedagogically advisable for our readers interested in Game Theory to start with classical Game Theory problems such as “The Prisoners Dilemma” and work their way to Cournot and Nash Equilibrium concepts.
