Simultaneous Game Theory is a branch of game theory that deals with games where players make decisions simultaneously. In this type of game, players don’t have any knowledge about the other player’s decision-making process. The game theory was first introduced by John von Neumann and Oskar Morgenstern in their book “Theory of Games and Economic Behavior” in 1944.

## What is Simultaneous Game Theory?

Simultaneous Game Theory is a type of game theory where all players make decisions simultaneously without having any knowledge about the other player’s decision-making process. This type of game is contrasted with Sequential Game Theory, where players make decisions one after another.

In Simultaneous Game Theory, each player has to choose a strategy from a set of strategies available to them. The outcome of the game depends on the combination of strategies chosen by all the players.

### Example:

Let’s take an example to understand Simultaneous Game Theory better. Consider two companies, A and B, who are deciding whether to advertise their products or not.

If both advertise, they will share the market equally, and if neither advertises, they will both get half of the market share. If one advertises and the other does not, then the company that advertises will get a larger market share than the company that did not advertise.

The table below shows the possible outcomes:

B Advertise | B Not Advertise | |
---|---|---|

A Advertise | 50-50 | 100-0 |

A Not Advertise | 0-100 | 50-50 |

In this example, both companies have two strategies: Advertise or Not Advertise. The results of the game depend on the combination of strategies chosen by both companies. For instance, if company A advertises and company B does not advertise, then company A will get a larger market share than company B.

### Nash Equilibrium:

Nash Equilibrium is a concept in Simultaneous Game Theory that describes a situation where no player can improve their outcome by changing their strategy unilaterally. In other words, Nash Equilibrium is a state where all players are satisfied with their current strategy, given the strategies chosen by other players.

In the above example, the Nash Equilibrium is when both companies advertise their products. If one company deviates from this strategy and decides not to advertise, they will get a smaller market share compared to the other company.

## Conclusion:

Simultaneous Game Theory is an essential concept in game theory that helps us understand how players make decisions in a game when they don’t have any knowledge about other players’ decision-making process. It’s used in economics, political science, psychology, and other fields to analyze different situations where multiple players are involved. By understanding Simultaneous Game Theory better, we can predict and analyze how different players might behave in different situations and make better decisions accordingly.