In economics, game theory is an important field of study 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 (i.e., individuals) are called players and each has a set of possible actions they can take. For example, in chess you have two players and each player has several possible actions or moves to choose from.

In a simple decision problem, an individual chooses the best option between several alternatives. The main difference between this and a game is that in a game, the payoff that the player gains from making a decision depends on the opponent's reaction. When a chess player moves a figure, they will try to predict how their opponent will react, and how they can counter that reaction. This series of decisions will influence the game’s outcome and the player’s chances of winning.

Of course, game theory isn’t only used to study real games like chess or Settlers of Catan. It’s also used to analyze any type of strategic interaction. For instance, in economics we use game theory to study how firms interact in a particular market.

Let us, for example, consider two main competitors in the airline industry - Lufthansa and United. When Lufthansa decides how to price their plane tickets, what kind of conditions to offer to their customers, or how to design new flight routes, they will need to predict how their customers are going to react to these decisions. This of course depends on the reaction of United. If Lufthansa raises ticket prices, United may counter by offering a promotion or simply not lowering prices, and gain more market share from Lufthansa as consumers switch over.

The market for passenger planes is not the only market in which a few or several firms compete. In oligopolistic markets, profit-maximizing 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 can also be used to study many other questions. For example, how do recommendations from other consumers influence consumption decisions? 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 applications of game theory and therefore it is 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 maximize benefits to themselves. Under this assumption, people do not make mistakes, and they are able to always make the optimal decision to maximize potential benefits. Increasingly in modern times, subfields such as behavioral economics relax this assumption and attempt to explain real-world decision-making.

Besides this, another common assumption in game theory is that the structure of the game and all of the information about the game is common knowledge. 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.

If the entire game and all of its attributes are common knowledge, then the players are said to have complete information. Similarly, 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; no one has incentive to deviate. One well-known example is the Prisoner’s Dilemma.

One of the most famous equilibrium concepts in game theory is the Nash equilibrium. But, there exist a variety of other solution concepts and refinements of the Nash equilibrium like 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. In many markets, for example, firms "meet" daily and compete by strategically choosing their prices or other instruments of competition.

Further reading

Given that game theory in economics is a broad field with many diverse applications, there are several excellent books available if you are interested in the topic in general. There are also a large variety of books on specific applications of the theory.

A gentle introduction to game theory can be found in Avinash Dixit and Barry Nalebuff's "The Art of Strategy". The book first covers some foundational concepts using some limited mathematics, and then turns to real-life examples like voting to illustrate game theory concepts.

For a more in-depth look at game theory, many modern textbooks cover the topic. You might also be interested in "Theory of Games and Economic Behavior" written by the mathematician John von Neuman and the economist Oskar Morgenstern, 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 including many social sciences. 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 may 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.