Pure Strategy

Definition

A pure strategy is a specific course of action that a player in a game chooses to follow consistently. It involves making a definite choice or decision at every stage of the game without randomness or mixed strategies. This concept is fundamental in understanding how players make decisions and predict outcomes based on the available information and their expectations of other players' actions.

5 Must Know Facts For Your Next Test

1. In a pure strategy, a player selects one action out of possible choices with certainty, without any element of chance.
2. Pure strategies can lead to predictable outcomes, making it easier for players to anticipate others' moves in games with complete information.
3. While pure strategies are straightforward, they may not always be optimal in every situation, especially when dealing with uncertainty or competition.
4. Games represented in normal form can have pure strategy Nash equilibria, where players settle into stable choices based on the actions of others.
5. The existence of pure strategies is not guaranteed in all games; some situations may only support mixed strategies for equilibrium.

Review Questions

• How does the use of pure strategies impact decision-making in games with multiple players?
  • The use of pure strategies simplifies decision-making by providing a clear, consistent choice for players. In games with multiple players, adopting a pure strategy means that each player's action remains fixed, allowing them to predict the likely responses of others. This predictability can lead to stable outcomes, as players adjust their strategies based on the expected actions of their opponents.
• Discuss the relationship between pure strategies and Nash equilibria in normal form games.
  • In normal form games, a Nash equilibrium can occur when players choose pure strategies that result in stable outcomes. At this equilibrium, no player benefits from unilaterally changing their strategy because they have chosen their best response given the strategies selected by others. The presence of pure strategy Nash equilibria indicates situations where players can reach an agreement or predictable outcome without resorting to mixed strategies.
• Evaluate the scenarios where using a pure strategy may not be advantageous for players and suggest alternative strategies.
  • Using a pure strategy may not be advantageous in scenarios characterized by uncertainty or competitive environments where opponents adapt their actions. In such cases, players might find themselves at a disadvantage if they are predictable. Alternatives like mixed strategies can introduce randomness into decision-making, allowing players to keep opponents guessing and potentially achieving better outcomes by exploiting unpredictability. Assessing the specific game's structure and opponents' behaviors can guide players toward the most effective strategic choices.

Related terms

Mixed Strategy: A mixed strategy involves a player randomizing over two or more pure strategies, assigning a probability to each strategy to keep opponents uncertain about their actions.

Nash Equilibrium: A Nash equilibrium occurs when each player's strategy is optimal, given the strategies chosen by others, meaning no player has anything to gain by changing their strategy unilaterally.

Dominant Strategy: A dominant strategy is one that yields a better outcome for a player regardless of what other players choose to do, making it the preferred choice for that player.