A pure strategy in game theory represents a choice of an available action in games in strategic form. It signifies a player's definitive commitment to a single, specific action, without any element of randomness or probability.
Understanding Pure Strategy
A pure strategy is a fundamental concept in game theory, particularly when analyzing how rational agents make decisions in interactive situations. As the reference states, it's a relatively straightforward concept, provided the notions of "availability" and "actions" are clear.
The Core Definition
At its heart, a pure strategy dictates that a player will select one specific action from their set of available choices. Unlike other strategy types, there's no probabilistic element involved; the player's choice is certain and predetermined. This concept is most commonly introduced and understood within the context of games in strategic form, also known as normal form games, which are typically represented by payoff matrices.
- Direct Choice: A player commits to a single, explicit action.
- No Randomization: There is no element of chance or probability in the decision-making process.
- Determinism: If a player adopts a pure strategy, their chosen action is predictable.
Pure Strategies in Different Game Forms
While the core definition primarily applies to games in strategic form, the concept of strategy extends to other game structures:
- Strategic Form Games (Normal Form): In these games, all players choose their actions simultaneously (or without knowledge of others' choices). A pure strategy is simply one of the specific actions listed for a player in the game's payoff matrix.
- Extensive Form Games: These games are played sequentially over time, represented by decision trees. In extensive games, a pure strategy is a complete plan that specifies an action for a player at every possible decision node they might encounter, even those that might not be reached if previous actions lead elsewhere. It's a comprehensive contingent plan.
Pure vs. Mixed Strategies
It's crucial to differentiate pure strategies from mixed strategies. The concept of strategy broadly includes both:
- Pure Strategy: As discussed, this involves choosing one specific action with 100% certainty.
- Mixed Strategy: This involves randomizing over two or more pure strategies, assigning a probability to each. For instance, a player might decide to choose action 'A' with a 70% probability and action 'B' with a 30% probability. This introduces an element of unpredictability to the player's actual move, even if the probabilities are known.
Practical Example: Rock-Paper-Scissors
Consider the classic game of Rock-Paper-Scissors.
If a player decides they will always choose "Rock" every time they play, this is a pure strategy.
- Player's Actions: Rock, Paper, Scissors
- Pure Strategy Example: Always choose "Rock"
- Another Pure Strategy: Always choose "Paper"
In contrast, if a player decides to choose "Rock" with 1/3 probability, "Paper" with 1/3 probability, and "Scissors" with 1/3 probability, this would be a mixed strategy.
Why Pure Strategies Matter
Pure strategies form the foundational building blocks for understanding more complex strategic interactions. Identifying pure strategies allows analysts and players to:
- Simplify Decision-Making: In games where a clear best choice exists without needing randomization, pure strategies provide straightforward solutions.
- Identify Dominant Strategies: Sometimes, one pure strategy is always better than any other, regardless of what other players do. This is known as a dominant pure strategy.
- Find Nash Equilibria: Many games have "pure strategy Nash Equilibria," where no player can improve their outcome by unilaterally changing their pure strategy, assuming others maintain theirs.
Understanding pure strategies is the first step towards grasping the broader spectrum of strategic thinking in various competitive and cooperative scenarios.
