science

N-player game

N-player game 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 N-player game rather than just read about it. In short: In game theory, an n-player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players.

Key takeaways

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

Reference excerpt

In game theory, an n-player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players. In defining n-player games, game theorists usually provide a definition that allow for any (finite) number of players. The limiting case of n → ∞ {\displaystyle n\to \infty } is the subject of mean field game theory. Changing games from 2-player games to n-player games entails some concerns. For instance, the Prisoner's dilemma is a 2-player game. One might define an n-player Prisoner's Dilemma where a single defection results everyone else getting the sucker's payoff. Alternatively, it might take certain amount of defection before the cooperators receive the sucker's payoff. (One example of an n-player Prisoner's Dilemma is the Diner's dilemma.)

Analysis n-player games can not be solved using minimax, the theorem that is the basis of tree searching for 2-player games. Other algorithms, like maxn, are required for traversing the game tree to optimize the score for a specific player.

References

Worked examples

Example 1 — a first encounter with N-player game

Start with the simplest possible case. Write down what N-player game 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 N-player game 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 N-player game 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 N-player game

In research: N-player game 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 N-player game 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: N-player game is common in secondary-school and first-year university syllabi. It links to neighbouring topics Economic theories stubs, Game theory game classes, Microeconomics stubs, so understanding it makes those chapters shorter.
In everyday life: Look for N-player game 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.

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How to study N-player game in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what N-player game 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 N-player game out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is N-player game in simple terms?

In game theory, an n-player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players.

Why does N-player game 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 N-player game?

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 N-player game.