# Pure strategies

## Understanding Pure Strategies

**Pure strategies**are defined as deterministic choices that players make in a game. This implies that a player sticks with one specific strategy throughout, regardless of the choices made by opposing players.- A game may have multiple pure strategies, and a pure strategy is not necessarily the best strategy. The
**effectiveness**of a pure strategy depends on the strategies used by the opposing player. - A deciding feature of a pure strategy is that it doesn’t involve any randomness or uncertainty. The player’s choice is fixed and the same choice will be made every time the game is played.

## Pure Strategies vs Mixed Strategies

- The core distinction between pure strategies and
**mixed strategies**lies in their level of determinism. Mixed strategies involve a level of randomness, in which a player decides to use different strategies according to specific probabilities. - The decision on whether to use a pure or mixed strategy depends on the game structure, including the pay-off matrix and the strategies employed by the other player.

## Use of Pure Strategies in Game Theory

- Pure strategies are valuable in the analysis of
**simultaneous move games**. Here, players pick strategies without the awareness of the opponent’s choice. - When players opt for pure strategies, the pay-off matrix simplification is possible, making the game easier to analyse and understand.
- In the context of the
**Nash equilibrium**, a pure strategy Nash equilibrium occurs when each player is making their best choice in response to the other players’ best choices.

## Pure Strategy Example: Prisoner’s Dilemma

- The
**Prisoner’s Dilemma**is a classic example used in game theory studies, and is often solved using pure strategies. - In this scenario, each player has a dominant pure strategy. Here, regardless of what the other player does, each player benefits more from confessing (a specific strategy) than from remaining silent.

Remember that the notion of a pure strategy is fundamental in game theory. Mastery of this concept will enhance your comprehension of more complex strategies and game scenarios.