Game theory is a branch of mathematics that studies decision-making in situations where multiple individuals or groups have competing interests. In a game theory game, players make choices based on the information available to them. These choices can impact not only the player themselves but also other players in the game.

There are three primary components of a game theory game: players, strategies, and payoffs.

## Players

In any game theory game, there must be at least two players. These players can be individuals or groups, and they can have conflicting or aligned interests.

For example, in a business negotiation, both parties are players in the game. Each player has their own set of options and potential outcomes that they are trying to achieve.

## Strategies

Each player has a set of strategies available to them. A strategy is simply a plan of action that a player can take based on the available information. Players choose their strategies based on what they believe will give them the best chance of achieving their desired outcome.

There are two types of strategies in game theory: pure strategies and mixed strategies. A pure strategy is when a player chooses one specific action every time they play the game. A mixed strategy is when a player randomly chooses between different actions based on probabilities.

## Payoffs

Finally, each player receives a payoff based on the outcome of the game. The payoff represents how much utility or satisfaction each player receives from the outcome.

The payoffs for each player depend on both their own strategy and the strategies chosen by other players in the game. In some cases, there may be multiple possible outcomes with different payoffs for each player.

### Example:

To illustrate these concepts further, let’s consider an example: rock-paper-scissors.

In this simple game, two players simultaneously choose one of three options: rock, paper, or scissors. Each option has its own strengths and weaknesses, and the outcome of the game depends on which options each player chooses.

– If both players choose rock, it’s a tie. – If both players choose paper, it’s a tie. – If both players choose scissors, it’s a tie.

– If one player chooses rock and the other chooses scissors, the player who chose rock wins. – If one player chooses paper and the other chooses rock, the player who chose paper wins. – If one player chooses scissors and the other chooses paper, the player who chose scissors wins.

In this game:

– The players are two individuals playing against each other

– The strategies are choosing between rock, paper, or scissors

– The payoffs depend on which option each player selects

### Conclusion

Understanding the three components of a game theory game is essential to effectively analyzing and predicting outcomes in strategic situations. By considering how players make choices, what strategies they use, and what payoffs they receive based on their choices, we can gain valuable insights into complex decision-making processes.