Game theory is a mathematical framework used to analyze and understand strategic decision-making in situations where the outcome depends on the choices of multiple individuals. It has applications in various fields such as economics, political science, psychology, and biology. In this article, we will discuss the basics of game theory and its key concepts.

## Players

In game theory, players are individuals or entities that make decisions. They could be individuals, groups of people, or organizations. Players are characterized by their preferences, which determine their choices.

## Strategies

A strategy is a plan of action chosen by a player to achieve their objectives. In game theory, strategies are determined by the player’s preferences and knowledge about other players’ preferences and strategies.

## Payoffs

A payoff is the result or outcome that a player receives from a specific combination of strategies played by all the players involved in the game. Payoffs can be positive or negative depending on whether they benefit or harm the player.

## Nash Equilibrium

Nash Equilibrium is a concept in game theory that describes a stable state of play where no player has an incentive to change their strategy given the strategies chosen by other players. It occurs when each player’s strategy is optimal given the strategies of all other players.

### Example:

Consider a scenario where two companies are competing for market share in an industry. If both companies choose to lower their prices simultaneously, they will end up earning less profit than if they both kept their prices high. However, if one company lowers its prices while the other keeps them high, then the former will gain more market share and earn higher profits while the latter loses market share and earns lower profits.

In this scenario, there are two strategies for each company: keep prices high or lower prices. The payoffs depend on what both companies choose to do.

If both companies keep prices high, they each earn $10 million in profit. If both companies lower their prices, they each earn $5 million in profit. If one company lowers its prices while the other keeps them high, the former earns $15 million and the latter earns $5 million.

The Nash equilibrium in this scenario is for both companies to keep their prices high as neither company has an incentive to change their strategy given the other company’s strategy. This is because if one company lowers its prices, it will lose profits while the other company gains market share and profits.

## Conclusion

Game theory provides a powerful framework for analyzing strategic decision-making in various fields. It helps us understand how players make decisions and how those decisions affect outcomes. By understanding the basics of game theory, we can gain insights into complex interactions between different entities and make better decisions based on those insights.