Pure strategy

A pure strategy is a plan where a player chooses one action with certainty instead of randomizing. In Intermediate Microeconomic Theory, it is the standard way to describe choices in static and dynamic games.

What is pure strategy?

A pure strategy in Intermediate Microeconomic Theory is a complete plan that tells a player exactly what action to take in every situation that can come up in a game. If you are using a pure strategy, you do not randomize. You pick one action and stick with it.

In a simple static game, that might mean choosing one price, one quantity, one bid, or one move at the same time as the other player. In a dynamic game, a pure strategy can be longer and more detailed, because it may tell you what to do after different possible past moves. The strategy is still pure as long as each decision is fixed rather than probabilistic.

The big contrast is with a mixed strategy, where a player uses probabilities across actions. In a pure strategy, there is no 70 percent here and 30 percent there. If your strategy says “always choose A,” then A is your pure strategy.

Pure strategies show up naturally when a best response is obvious and does not depend on randomization. For example, if one action strictly beats another for every possible choice by the other player, that action is a dominant strategy and it is usually written as a pure strategy. In a payoff matrix, you often identify pure strategies by checking whether a player has a single best action in each column or row.

A useful way to think about it is this: a pure strategy is the full rule, not just one isolated move. The point is not just what you do today, but what you would do in every relevant situation the game could produce. That is why pure strategies are the starting point for Nash equilibrium analysis, especially when the equilibrium happens without randomization.

Why pure strategy matters in Intermediate Microeconomic Theory

Pure strategy is the easiest way to pin down behavior in game theory problems, so it shows up early and often in Intermediate Microeconomic Theory. If you can identify pure strategies, you can usually work faster through payoff matrices, dominant strategy questions, and Nash equilibrium checks.

It also gives you a clean way to interpret strategic behavior. When both firms in a duopoly choose one output level, or both players in a simple pricing game stick to one action, you are looking at pure-strategy reasoning. That makes it easier to compare outcomes, see who has bargaining power, and spot when a player has no incentive to deviate.

Pure strategy also matters because not every game has a pure-strategy equilibrium. When no single fixed action is stable, you have to move to mixed strategies. So knowing pure strategy is part of knowing when the simple answer works and when the model forces you to randomize.

In class problems, the term helps you read strategy profiles correctly. You are not just naming an action, you are checking whether that action is part of a stable outcome under the rules of the game.

How pure strategy connects across the course

Mixed strategy

Mixed strategy is the main contrast to pure strategy. Instead of choosing one action with certainty, a player assigns probabilities to multiple actions. You usually switch to mixed strategies when no pure strategy gives a stable best response, which is common in matching pennies style games or other situations where randomization changes the opponent’s incentives.

Nash equilibrium

Pure strategies often appear inside Nash equilibrium when every player is making a fixed best response to everyone else. If a game has a pure-strategy Nash equilibrium, you can identify it by checking that no one wants to change actions unilaterally. Not every Nash equilibrium is pure, but pure-strategy equilibria are the first ones many problems ask you to find.

Dominant strategy

A dominant strategy is stronger than just a pure strategy. It is a fixed action that gives a player the highest payoff no matter what the other players do. Many dominant strategies are pure, and when one exists, it can make equilibrium analysis much simpler because you do not need to compare every possible opponent move.

Payoff Matrix

A payoff matrix is where you usually spot pure strategies in a two-player static game. Each row and column lists fixed actions, so you can compare payoffs and see whether a player has one best response. The matrix format makes it easier to check for pure-strategy Nash equilibria and dominant strategies.

Is pure strategy on the Intermediate Microeconomic Theory exam?

A problem set or quiz question will usually ask you to identify each player’s pure strategy set, then test whether a particular action profile is a Nash equilibrium. You may also be asked to compare pure and mixed strategies in a payoff matrix, or explain why a game has no pure-strategy equilibrium. In a dynamic game question, you might write out a strategy that specifies what a player does after different possible past moves, then check whether that strategy is still pure because it gives one fixed action in each case. The key move is to look for certainty, not probabilities.

Pure strategy vs mixed strategy

These are often confused because both describe how a player behaves in a game. A pure strategy picks one action with certainty, while a mixed strategy randomizes across actions using probabilities. If you see a player choosing 100 percent A, that is pure. If you see 60 percent A and 40 percent B, that is mixed.

Key things to remember about pure strategy

• A pure strategy is a fixed plan of action, not a random choice.

• In Intermediate Microeconomic Theory, pure strategies are the basic building blocks of static and dynamic games.

• A pure strategy can be part of a Nash equilibrium if no player wants to change their action alone.

• Pure strategies are easier to check in payoff matrices because you compare clear best responses.

• If no pure strategy works, the game may require mixed strategies instead.

Frequently asked questions about pure strategy

What is pure strategy in Intermediate Microeconomic Theory?

A pure strategy is a player’s fixed choice of action in a game, with no randomization. In micro theory, you use it to describe exactly how someone behaves in a strategic setting, like choosing one price, one output level, or one move in a payoff matrix.

How is pure strategy different from mixed strategy?

Pure strategy means one action is chosen with certainty. Mixed strategy means the player randomizes across two or more actions using probabilities. The distinction matters because some games have a pure-strategy Nash equilibrium, while others only work if players mix.

How do I find a pure strategy Nash equilibrium?

Start by checking each player’s best response to the other player’s actions. If you find an action profile where every player is already choosing a best response, that profile is a pure-strategy Nash equilibrium. If no such profile exists, the game may need a mixed-strategy solution.

Can a pure strategy change over time in a dynamic game?

Yes. In a dynamic game, a pure strategy can be a complete plan that tells you what to do at each point in the game, based on the history that could occur. It is still pure as long as each decision is fixed rather than probabilistic.