science

Mutual knowledge

Mutual knowledge is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Mutual knowledge rather than just read about it. In short: Mutual knowledge in game theory is information known by all participatory agents. However, unlike common knowledge, a related topic, mutual knowledge does not require that all agents are aware that this knowledge is mutual.

Key takeaways

Mutual knowledge belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Mutual knowledge to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Mutual knowledge from memory before moving on to harder problems.

Reference excerpt

Mutual knowledge in game theory is information known by all participatory agents. However, unlike common knowledge, a related topic, mutual knowledge does not require that all agents are aware that this knowledge is mutual. All common knowledge is mutual knowledge, but not all mutual knowledge is common knowledge. Mutual knowledge can arise accidentally, due to a failure to design the game properly, so all players independently discover this mutual knowledge, or deliberately, due to the expected course of the game.

The difference between mutual knowledge and common knowledge The difference is crucial in a co-operation game. For example, in the game depicted below, with a random event determining the payoff matrix, both players, being fully rational, presume the more likely option to have occurred. However, suppose each player separately finds out that the random number, which was created privately and which determines the payoff matrix, was 1. However, neither are told that the other player is also aware of this. Player A presumes Player B is not aware the random number is 1. They then observe that if the random number is 2-100, the best choice for B is always b1. So they choose a2, which would give them the best possible payoff in this matrix. Symmetrically, Player B presumes Player A expects the random numbers 2-100 and chooses a1, so B chooses b2. As a result, the players had a final result of (1, a2, b2), with a payoff of 1 for both - the lowest possible payoff (total or individual). Now suppose that it is common knowledge that the random number is 1 - that is, both players are also aware that the other player knows the random number is 1, in addition to knowing this themselves. Given this, the best choice for A is a1, with an average of 6.5, and the best choice for B is b1, with an average of 6.5 also, giving an outcome of (1, a1, b1) with a payoff of 8 for both - the highest possible total payoff. Common knowledge tends to lead to co-operative behavior more often than purely mutual knowledge, which can often lead to anti-cooperative behavior as shown in the example above, as the participants are aware that the knowledge is mutual knowledge and can all decide on behalf of this knowledge. This works best in a symmetric game, like the left matrix below.

Bibliography

Worked examples

Example 1 — a first encounter with Mutual knowledge

Start with the simplest possible case. Write down what Mutual knowledge claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Mutual knowledge before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Mutual knowledge ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Mutual knowledge

In research: Mutual knowledge appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Mutual knowledge in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Mutual knowledge is common in secondary-school and first-year university syllabi. It links to neighbouring topics Economic theories stubs, Game theory, Microeconomics stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Mutual knowledge outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Mutual knowledge” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Mutual knowledge in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Mutual knowledge means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Mutual knowledge out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Mutual knowledge in simple terms?

Why does Mutual knowledge matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Mutual knowledge?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Mutual knowledge.