What is game theory?: a basic introduction

Recently I noticed in movies and TV shows, game theory is being mentioned and it struck me that I don’t know what game theory is. So here I am researching it and sharing what I learned with you. First, let me say that there is so much more to game theory than what I can write about without being long winded or boring. I will only cover the basics. That being said, here we go. Game theory is the study of mathematical models of conflicts and cooperation between intelligent rational decision makers. It is mainly used in economics, political science and psychology. It can also be applied to logic, computer science and biology.

The first known discussion of game theory occurred in letter to James Waldegrave, a British diplomat from Charles Waldegrave, his uncle, in 1713. Known as the Waldegrave problem, it was a mixed strategy solution to a two-person card game called le Her in which a standard deck of 52 cards are played between a dealer and a receiver. James Madison used what is now called game theoretic analysis to predict how the states can be expect to act under different taxation systems (Vice of the Political System of the United States, April 1787). Throughout the years, many other theories devised their own game theories. In 1838, Antoine Augustin Cournot used duopoly, a form of oligopoly where only two sellers exist in one market, and presented a solution to the Nash equilibrium. The Nash equilibrium is a solution concept of a non-cooperative game. The study of game theory didn’t truly exist as its own field until 1938. While there are many game types in game theory, I will be discussing three.

First, cooperative versus non-cooperative games. In cooperative game theory, players are able to form binding commitments externally enforced, i.e. contract law. The focus is on predicting which coalitions will form place and the resulting payoffs. Cooperative game theory does not focus on how coalitions achieve their payoffs. For example, a coalition can exchange whatever it wants among its members; however, it does not discuss how offers or counteroffers are made. The image of a bargaining table in which two or more people are hashing out a business deal or even a criminal plea deal. Non-cooperative game theory, players cannot form alliances or if all agreements need to be self-enforcing, i.e. credible threats. The focus is on predicting individual players’ actions and the possible payoffs while trying to predict what strategies the players will choose. In essence how people should or do act for the maximum individual benefit.

Second, symmetric versus asymmetric game theory. In symmetric game theory, payoffs for playing a particular strategy depends only on the other strategies played and not who played them. If the players changed without changing the strategies, the playoffs would be the same. The game of chicken is an example of a symmetric game. Each player has two decisions to yield or not. Regardless who yields and who doesn’t, the payoff is the same. If one player yields, the other player should not yield. If one player won’t yield, the other player should. In asymmetric game theory, there are no identical strategy sets for both players. For example, the ultimatum game which is used in economic experiments. One player receives a sum of money and proposes how to divide the money. If player two accepts the proposal, the money is split according to the proposal. If player two rejects the proposal, neither player receives any money.

Third, zero sum versus non zero sum game theory. In zero sum game theory, the choices made by the players can neither increase nor decrease the available resources. The total benefit to all players always adds to zero. In other words, a player only benefits at the expense of another. Chess is an example of a zero sum game as one player benefits when the other player loses a piece or cannot make another move. In a non-zero sum game, the outcomes results are greater or less than zero. A gain by one player does not necessarily correspond with another player’s loss. In layman’s terms, it is a win-win situation. One example is The Prisoner’s Dilemma. It is the problem faced by two accomplices locked in separate cells. Each is offered three choices by the police: one, they can both confess to the charges, both will be jailed for five years. Two, if only one confesses, he will be freed but the non-confessor will be jailed for ten years. Or three, if neither confesses, both will be tried for a minor offense and will be jailed for one year. If both prisoners know that the other will not confess, neither will confess and serve one year in jail. It’s a win-win for both prisoners.

In conclusion, game theory is, at its core, about prediction. Predictions of behavior, strategies, decision making and payoffs. It is about keeping an equilibrium or balance. It is about human conflicts and cooperation within competitive or game situations. It is about optimal decision making for the best outcomes for all involved or one individual over another. The theory is applied to many games we play: chicken, chess, poker and other situations where decisions are made for the best outcomes. It is a very simplified explanation and only hits the tip of the iceberg when it comes to what game theory is and how it is used. I’m curious to read further and hope it was informative for you, if you were unaware of what game theory is.