Does searching deeper reveal private information?

No; computation cannot directly observe withheld facts.

Must a good strategy randomize?

Not always; the particular game and objective determine that.

AI Glossary / Graphs and symbolic AI / Advanced

Imperfect information

Definition

Imperfect information is a condition in a game where a player making a decision cannot distinguish all relevant situations that may have occurred. Some past actions or parts of the current state are hidden. The player's strategy must use the information actually available, rather than the complete state visible to an outside observer.

What it means

Poker illustrates the idea because an opponent's cards are private. Knowing the rules and seeing the public actions does not reveal the entire position. Uncertainty remains when a player must choose what to do.
Imperfect information is different from simply being unable to predict the future. Under the standard extensive-form definition, a game can include chance moves and still have perfect information if players observe the realized history whenever they act. Unknown future dice rolls do not themselves hide an already realized event.
A difficult game is not necessarily an imperfect-information game. Chess can demand enormous calculation even though the board and previous moves are observable.

How it works

An extensive-form model represents possible histories as nodes in a game tree. An information set groups decision nodes that the player cannot distinguish using the observations available at that moment.
At nodes in the same information set, the player must use the same action rule, including the same probability distribution if randomizing. Otherwise, the model grants the player access to hidden information.
An agent may maintain beliefs over possible hidden histories and update them when new observations arrive. In strategic settings, interpreting an observed action can depend on a model of the other player's behavior. Beliefs are not automatically uniform, and their accuracy should not be assumed merely because they are expressed numerically.

Three practical examples

A card-playing agent chooses whether to continue after observing a public bet. It may reason about possible private cards, but it cannot condition its actual decision on a card it has not seen.
A competitive simulation asks two agents to choose routes without revealing the other's selection. The simulator knows both routes; each participating agent receives only the observations allowed by the rules.
A training exercise models a rival's hidden production choice. Analysts compare a policy based on observable signals with an idealized policy that sees the choice.

Think of it this way

Imagine choosing a door while someone else knows what is behind each one. An outside analyst can describe the best choice for every hidden arrangement. You still need one decision rule that works with what you can actually observe.

Worked example

Consider an invented two-player game. Player One secretly selects A or B. Player Two then chooses X or Y without seeing that selection. Both players know the payoff table. Player Two receives 6 for X against A, minus 2 for X against B, minus 3 for Y against A, and 4 for Y against B. Player One receives the negative of that payoff.
The two possible decision nodes for Player Two belong to one information set. A proposed rule saying “choose X after A and Y after B” is unavailable because the hidden selection is not observed.
First suppose Player Two has a justified model that Player One chooses A with probability 0.6 and B with probability 0.4. Choosing X gives expected payoff 0.6 times 6 plus 0.4 times minus 2, which equals 2.8. Choosing Y gives 0.6 times minus 3 plus 0.4 times 4, which equals minus 0.2. X is better against this specified model.
An observer who sees the hidden selection could choose X after A and Y after B, receiving an expected 5.2. Reporting 5.2 as the achievable value without observation would give Player Two information the rules withhold.
Now remove the assumed probabilities and ask for protection against an adversarial selection. Let q be the probability of choosing X. The expected payoff against A is 9q minus 3; against B it is 4 minus 6q. Equalizing them gives q = 7/15 and a payoff of 1.2 against either selection.
This is the maximum guaranteed expected payoff: below 7/15 the payoff against A is less than 1.2, and above it the payoff against B is less than 1.2. The guarantee concerns expectation, not every individual play. It also assumes the opponent does not observe Player Two's realized random choice before selecting.
Thus the preferred action rule depends on whether the objective is exploiting a specified opponent model or protecting against an unrestricted adversary. Hidden information does not supply either objective automatically.

Illustrative case study

Fictional Cedar Games evaluates an agent in a hidden-route contest. Its first evaluator solves each complete simulated state separately and credits the agent with the best response for that state.
A reviewer notices that two states look identical to the agent but receive different recommended actions. The evaluator has silently used the rival's hidden route.
Cedar rewrites evaluation around the agent's observation history and restricts decisions to that history. It keeps the fully informed result as a separately labeled comparison. Reviewers also test whether changing hidden simulator fields can alter an action when the visible history is unchanged.

Common misconceptions and mistakes

“Imperfect information means random outcomes.” Hidden observations and chance are distinct features.
“A simulator knows the state, so the agent may use it.” Access must follow the game's observation rules.
“Hidden possibilities are equally likely.” That needs justification.
“A randomized strategy wins every round.” Expected guarantees permit individual losses.
“Remembering everything gives perfect information.” Perfect recall does not reveal information never observed.

Business use

Specify exactly what each participant observes and when. Keep private information separate from public signals in both training and evaluation.
Report whether a strategy is assessed against a fixed behavioral model or a strategic opponent that may adapt. Test sensitivity to changed assumptions, and label fully informed comparisons clearly. Otherwise, an apparently strong result can reflect unavailable information rather than a usable decision policy.

Check your understanding

Why is the 5.2 policy unavailable?

Answer: It conditions decisions on the hidden selection.

What does 1.2 guarantee?

Answer: Expected payoff against either opposing selection under the stated timing.

Why can two tree nodes share an information set?

Answer: The player cannot distinguish their histories.

Related terms

Information sets
Perfect information
Game theory
Information set
perfect recall
behavioral strategy
hidden state
belief

Learn next

Draw the worked example's tree, join the indistinguishable decision nodes, and compare the original game with a version that reveals the selection before Player Two acts.

Decision nodes

Sources

AIMA glossary, imperfect information: https://github.com/aimacode/aima-glossary/blob/master/glossary.md Thomas S. Ferguson, Game Theory, Part II, extensive-form games: https://www.cs.cmu.edu/afs/cs/academic/class/15859-s05/www/ferguson/mat.pdf Andrew Gilpin, Algorithms for Abstracting and Solving Imperfect Information Games: https://www.cs.cmu.edu/~gilpin/papers/thesis.pdf

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