# Game Theory

A mathematical framework developed to address problems with conflicting or cooperating parties

## What is Game Theory?

Game theory is a mathematical framework developed to address problems with conflicting or cooperating parties who are able to make rational decisions. The theory primarily deals with finding the optimal rational decision in various scenarios.

Game theory is a relatively new discipline. Modern game theory was introduced in the works of John von Neumann in the 1920s. Von Neumann, Oskar Morgenstern, and John Nash were the main contributors to the development of game theory. The theory offers a wide number of applications in different fields, including economics, political science, finance, psychology, and biology, among others.

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### Game Theory Applications in Finance

A game theory framework can be applied in different areas of finance, including corporate finance, portfolio management, and investment banking. Some of the most popular areas of game theory application are the following:

• Asset pricing
• Mergers and acquisitions (M&A)
• Capital structure
• Corporate governance

### Classifications in Game Theory

Game theory classifications are related to several settings. The scenarios examined include the following:

#### 1. Cooperative/Non-cooperative

This is probably the most common type of game discussed in game theory. In cooperative game settings, the participating players can form binding agreements with each other, and decisions are made by a coalition (a group of players). The decision made by a coalition leads to the payoff that should be distributed among the players.

On the other hand, a non-cooperative game considers situations where players cannot form binding agreements. The non-cooperative game theory analyzes possible strategies and payoffs of individual players to determine a Nash equilibrium.

#### 2. Symmetric/Asymmetric

A symmetric game deals with a game setting in which the payoffs primarily depend on the strategy chosen by each player, not on other players’ choices. In an asymmetric game, the payoffs vary among the players. Thus, even if the players employ the same strategy, their payoff will be different.

#### 3. Zero-sum/Non-zero-sum

In a zero-sum game, the gains/losses of one player are balanced with the losses/gains of other players. In non-zero-sum games, the gains/losses of one player do not result in the losses/gains of other players. In other words, a non-zero-sum game may result in a win-win situation.

#### 4. Simultaneous/Sequential

In a simultaneous game, all the participating players make their decisions simultaneously, or they make their decisions without the knowledge of the decisions of other players. In a sequential game, the players take turns to make decisions or have information about the decisions of other players.

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#### 5. Perfect information/Imperfect information

The perfect information game considers the situation when all the players are able to access the same information with which to make their decisions. In contrast, in an imperfect information game, the information that is available to one player is inaccessible to the other players.