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.