In game theory, a pooling equilibrium is a strategy in which all players adopt the same action. It is a type of equilibrium where the players in the game are indistinguishable from one another. This means that each player has no incentive to deviate from the chosen strategy, as doing so would not give them any advantage.

## What Is Game Theory?

Game theory is a branch of mathematics that studies decision-making in situations where two or more individuals or groups are involved. It is used to analyze and understand human behavior and interactions in various fields, such as economics, politics, psychology, and biology.

## Types of Equilibria

In game theory, there are different types of equilibria that can occur in a game:

- Nash equilibrium
- Pareto equilibrium
- Stackelberg equilibrium
- Pooling equilibrium

### Nash Equilibrium

A Nash equilibrium is a situation where each player’s strategy is optimal given the strategies chosen by all other players. In other words, no player can benefit by changing their strategy while the others keep theirs unchanged.

### Pareto Equilibrium

A Pareto equilibrium is a situation where no player can be made better off without making another player worse off. In other words, it is an outcome that maximizes the total welfare of all players.

### Stackelberg Equilibrium

A Stackelberg equilibrium is a situation where one player (the leader) chooses their strategy first, and then the other player (the follower) chooses their strategy knowing what the leader has chosen.

### Pooling Equilibrium

A pooling equilibrium is a situation where all players adopt the same action or strategy. It occurs when there are multiple equilibria in a game, and all players choose the same one.

## Example of Pooling Equilibrium

An example of a pooling equilibrium is the “matching pennies” game. In this game, there are two players, and each player can choose to show either a “heads” or “tails” side of a coin. If both players show the same side, then one player wins; otherwise, the other player wins.

In this game, there are two equilibria: (1) both players show “heads,” and (2) both players show “tails.” These are both pooling equilibria because all players adopt the same strategy. No player has an incentive to deviate from their chosen strategy because doing so would not give them any advantage.

## Conclusion

Pooling equilibrium is an important concept in game theory that can help us understand decision-making in situations where all players adopt the same strategy. Understanding these types of equilibria can provide valuable insights into human behavior and interactions in various fields.