Economics Terms A-Z

Game Theory

By

Game theory is an important field of study in economics that focuses on the interaction of several decision makers that act strategically. A game refers to any type of situation in which the payoff or utility that an individual can gain by making a decision depends not only on their decision but also on the decision of others.

In game theory the decision makers or individuals are called players and each has a set of possible actions they can take. For example, in a chess game you have two players (one playing black and the other white) and each player has several possible actions or moves to choose from. In chess the white player may open the game by moving any of the pawns or may choose to move one of their two horses. The main difference between a game and a simple decision problem where an individual chooses between several alternatives, is that in a game the payoff that the player gains from making a decision depends on the reaction of the opponent. When a chess player moves a figure they will try to predict how their opponent will react and how this in turn will influence the game and their chances of winning.

Of course, game theory isn’t only used to study real games like chess. It’s also used to analyse any type of strategic interaction. In economics we use game theory to study how firms interact in a particular market. Let us, for example, consider the aviation market in which we have two main competitors - Boeing and Airbus. When Airbus decides how to price their plane tickets, what kind of conditions to offer to their customers or how to design new types of aircrafts, they will need to predict how their customers are going to react to these decisions and this of course depends on the reaction of Boeing. The market for passenger planes is not the only market in which a few or several firms compete. In oligopolistic markets, profit-maximising firms take into account the strategies of other firms when they decide how to price a product, whether to launch a new marketing campaign, how much to invest in R&D, and so forth. Besides competition between firms, game theory is also used to study the behaviour of consumers. For example, how do recommendations from other consumers influence consumption decisions? Other questions that are analysed using game theory include: how can employees be incentivized to exert effort? Is it possible to achieve cooperation among members of a team? And how should politicians design their campaigns if they want to attract as many voters as possible? As you can see from these examples, there are many economic applications of game theory and therefore it became a very important field of research in economics.

It is assumed in game theory that actors act rationally, that is, that they act in order to maximise benefits to themselves. (Some ideas, such as those of behavioural economics, oppose this assumption.) Besides this, another important assumption in game theory is that the structure of the game and all (or most) of the information is common knowledge. A piece of information is common knowledge if everyone knows that everyone knows that everyone knows ad infinitum, this information. For example, if Anne and Bob play a game and both are rational and it is common knowledge that both are rational then this means that Anne knows that Bob is rational and Bob knows that Anne is rational. But it does not end here. Anne does not only know that Bob is rational, she also knows that Bob knows that she (Anne) is rational, and so forth. If the entire game with all its features is common knowledge then the players are said to have complete information. Information is incomplete if certain features of the game are not common knowledge. Examples may include situations in which one player does not know all the possible moves the other player could make; when a player does not know who their competitor is; or when a player does not know how payoffs relate to their actions.

The game finishes when equilibrium is reached, meaning after all players have made their decisions and the outcome has become clear. Equilibrium of a game refers to a situation in which no player wants to change their strategy given the strategy of the other players. That is, no one wants to deviate from the current situation. One of the most famous equilibrium concepts is the Nash equilibrium, but there exist a variety of other solution concepts and refinements of the Nash equilibrium like, for example, the Bayes-Nash-equilibrium, the sub-game perfect Nash equilibrium, the trembling-hand perfect equilibrium and many more.

Games can be classified according to their structure, the information that the players have, or the time horizon of the game. Whether players choose their actions at the same time or one after the other determines if it’s a simultaneous-move or sequential game. One-shot games are games in which players interact only once, while a repeated game is a game in which players interact in several time periods, i.e., repeatedly. In many markets, for example, firms meet each daily and compete by strategically choosing their prices or other instruments of competition.

Further reading

Given that game theory is a broad field with many diverse applications, there are several excellent books available if you are interested in the topic in general, while there is also a large variety on particular applications or more specific topics. A good place to start is “Theory of Games and Economic Behavior” written by the mathematician John von Neuman and the economist Oskar Morgenstern, and published in 1944. It’s one of the first game theory books ever written and is a classic in the field.

Good to know

Game theory is not only used in economics but also applied in a variety of other fields mainly in the social sciences but also beyond. In biology, for example, game theory is used to study population dynamics (reproduction, mutation and extinction). This branch of game theory is called evolutionary game theory and was pioneered by John Maynard Smith. Psychologists as well as neuroscientists apply game theory in their experiments and studies. Besides this, game theory approaches are used in mathematics, the political sciences, management, and the fields of operations research, electrical engineering and computer sciences.