# Game theory

**Game theory** is the mathematical study of strategy and decision-making. Most discussions in game theory focus on games of strategy that assume rational actors: that is, that the participants take the course that offers them the best outcome reasonably available under the circumstances.

Although game theory is a field of mathematics, it is often applied to the subject matter of other disciplines, most notably economics, but also many others including political science, computer science, and evolutionary biology. It provides models for behavior in diverse situations by modeling interactions among participants and evaluating the possible outcomes of those interactions and what utility each participant receives.

## History of game theory

The development of game theory as a distinct field within mathematics is attributed to John von Neumann, a Hungarian-born mathematician who began publishing papers on the theory of games in 1928. In 1944, he and Oskar Morgenstern published *Theory of Games and Economic Behavior*, a book that is credited as the ground-breaking work of the field.

## Types of Games

## Simple example: The prisoner's dilemma

A case study in game theory is perhaps the best-known example: The Prisoner's Dilemma. Two prisoners are being interrogated separately, suspected as accomplices for the same crime. If neither confesses, they face only a short sentence of length A. If one betrays the other, that prisoner goes free while the other prisoner gets a very lengthy sentence (B). If both betray their partner, they both get a medium-long sentence (C). Sentence A < C <B.

The outcome with the least prison time is one of dual-silence. However, since each individual patient is better served by going free (as opposed to serving sentence A), and would rather serve sentence C than B (if the partner betrays them), it makes the most sense for each individual prisoner to betray, regardless of the action of their accomplice.

## Symmetry

In the above example of the Prisoner's Dilemma, both players have exactly the same choices and the same outcomes. Games like this are said to be symmetric, as the roles each player plays are identical. In other games, each player's role is different. For instance, one player might make an offer, which the other player either accepts or rejects. These games are asymmetric.

## Zero-sum games

A zero-sum game is one in which one player can only benefit at the equal detriment of the other. In this case, the gains and harms in each decision add up to zero.

## Iterated Games

While some games are only played once, others are played multiple times consecutively. This introduces the history into the decision-making logic In the above Prisoner's Dilemma example, knowing whether your partner was faithful or not previously might have an impact on a player's decision.