Is a strategy the same as a policy?

The terms overlap in AI, but strategy commonly emphasizes interaction with other decision-makers; the exact mathematical setting matters.

Must a strategy include unlikely situations?

A complete strategy specifies actions at every relevant information set, even ones not reached in a particular play.

Does a mixed strategy mean uncertainty about what I want?

No. It can mean deliberately randomizing actions while pursuing a clearly defined payoff objective.

AI Glossary / Graphs and symbolic AI / Beginner

Strategy

Definition

A strategy is a player's complete plan for choosing actions in a game or other model of strategic interaction. A pure strategy specifies an action at every decision situation the player can distinguish. A mixed strategy assigns probabilities to pure strategies. In AI, strategies help describe agents whose results depend on the choices of other agents.

What it means

In everyday business language, strategy can mean a broad ambition such as entering a market. In game theory, it has a more precise role: it tells the model what a player would do in each relevant circumstance. “Improve customer service” is an objective; a specified response to each possible customer or competitor action can form part of a strategy.

A strategy is different from the action observed in one play. Two players may make the same visible choice while following different plans for circumstances that did not occur. Those differences can matter when evaluating alternatives, threats, or future interactions.

How it works

First define the players, available actions, information, timing, and payoffs. Then identify each player's information sets: decision situations the player cannot distinguish from one another belong together. A feasible pure strategy must choose the same action across situations within one information set.

For a finite sequential game, list an action for every relevant information set, including ones not reached during a particular play. For a simultaneous one-move game, a pure strategy may simply be one available action.

To evaluate a strategy, combine it with the other players' strategies and the game's chance rules. This determines an outcome or a distribution over outcomes. Randomization can be represented by a probability distribution over complete pure strategies; probabilities must be nonnegative and add to one. Whether a strategy is attractive depends on the objective and the assumptions about other players.

Three practical examples

Negotiation simulation: an agent specifies whether to accept, reject, or counter each offer it might receive within a bounded bargaining game.
Cybersecurity exercises: a defender chooses inspection patterns while accounting for an attacker who can adapt to predictable checks. This is an authorized simulation, not a claim about real attack outcomes.
Shared-resource coordination: several software agents choose when to request a limited resource, making each agent's outcome depend on the others' timing choices.

Think of it this way

Think of a strategy as a branching instruction card that covers every situation a player could recognize. The card remains complete even when only one branch is followed. The analogy stops where real games require enormous or continuous decision spaces: a strategy may be represented by a function or algorithm rather than a literal list of instructions.

Worked example

Consider an original two-stage toy game. Player One chooses Left or Right. Player Two observes that choice and then chooses Up or Down. Player Two therefore has two distinct decision situations.

Write Player Two's pure strategy as an ordered pair: the first action applies after Left and the second after Right. The four strategies are (Up, Up), (Up, Down), (Down, Up), and (Down, Down). If Player One chooses Left, the first two strategies both produce Up. Observing that outcome does not reveal which complete strategy Player Two followed.

Now change only the information rule: Player Two cannot observe whether Left or Right occurred. The two decision situations belong to one information set. Only two pure strategies remain: always Up and always Down. The contingent plan “Up after Left, Down after Right” is no longer implementable using the information provided.

Suppose a separate randomizing device selects always Up with probability 0.7 and always Down with probability 0.3. This defines a mixed strategy, not a promise that exactly seven of every ten realized actions will be Up. No payoffs have been supplied, so this calculation establishes feasible strategy choices, not which choice is optimal or an equilibrium.

Illustrative case study

Fictional case: a training company builds a negotiation exercise with an AI buyer. Its first specification says only “accept a reasonable price.” Testers cannot reproduce decisions because reasonable is undefined and the buyer's information changes between rounds.

The team specifies visible offer history, allowed counteroffers, and a response rule for every recognized situation in the exercise. It also records what happens when no agreement is reached. The exercise now distinguishes the buyer's objective from its action-selection strategy. This fictional example illustrates clearer modeling; it does not claim that the resulting strategy earns more profit or negotiates fairly.

Common misconceptions and mistakes

A strategy is not necessarily clever, successful, or rational: even a consistently poor complete plan is a strategy. A realized sequence of actions does not always identify the underlying plan. Conditioning on a hidden fact creates an infeasible strategy unless the player has a legitimate way to observe or infer the required information.

Randomizing without specifying probabilities leaves a mixed strategy incomplete. Equally, an equilibrium is not one player's strategy in isolation; it concerns how the players' choices fit together under a stated solution concept.

Business use

For business modeling, separate objectives, information access, feasible actions, and response rules before comparing automated agents. Ask which choices change when competitors, customers, or suppliers respond differently. Preserve the assumptions behind simulations: an impressive strategy against one fixed opponent may perform differently against an adaptive one.

When implementation is involved, test whether the software can actually observe every variable on which its strategy depends.

Check your understanding

A player cannot distinguish two decision nodes. Can its pure strategy prescribe different actions at those nodes?

Answer: No. They form one information set, so the strategy must prescribe one feasible action for that information set.

Related terms

Strategy profile
Pure strategy
Mixed strategy
Information sets
Policy
information set
best response
Nash equilibrium
extensive-form game

Learn next

Draw a small decision tree and label what each player observes. Count each player's pure strategies before and after hiding one observation. Then add payoffs and study best responses, keeping feasibility separate from desirability.

Decision tree

Sources

Yale, Ben Polak, Game Theory Lecture 18, information sets and complete contingent strategies: https://oyc.yale.edu/economics/econ-159/lecture-18 Carnegie Mellon, 15-281 Game Theory course notes, strategic interaction and mixed strategies: https://www.cs.cmu.edu/~15281/coursenotes/gametheory/ Scope: formal game-theoretic meaning. The numerical scenario and fictional case are original teaching examples.

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