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Intransitive game

Intransitive game is a mathematics 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 Intransitive game rather than just read about it. In short: An intransitive or non-transitive game is a zero-sum game in which pairwise competitions between the strategies contain a cycle. If strategy A beats strategy B, B beats C, and C beats A, then the binary relation "to beat" is intransitive, since transitivity would require that A beat C.

Key takeaways

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

Reference excerpt

An intransitive or non-transitive game is a zero-sum game in which pairwise competitions between the strategies contain a cycle. If strategy A beats strategy B, B beats C, and C beats A, then the binary relation "to beat" is intransitive, since transitivity would require that A beat C. The terms "transitive game" or "intransitive game" are not used in game theory. A prototypical example of an intransitive game is the game rock, paper, scissors. In probabilistic games like Penney's game, the violation of transitivity results in a more subtle way, and is often presented as a probability paradox.

Examples Rock, paper, scissors Penney's game Intransitive dice

See also Stochastic transitivity

References Gardner, Martin (2001). The Colossal Book of Mathematics. New York: W.W. Norton. ISBN 0-393-02023-1. Retrieved 15 March 2013.

Worked examples

Example 1 — a first encounter with Intransitive game

Start with the simplest possible case. Write down what Intransitive game claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, 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 Intransitive 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 Intransitive 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 Intransitive game

In research
Intransitive game appears in mathematics 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 Intransitive 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
Intransitive game is common in secondary-school and first-year university syllabi. It links to neighbouring topics Applied mathematics stubs, Zero-sum games, so understanding it makes those chapters shorter.
In everyday life
Look for Intransitive 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 Intransitive game in 20 minutes

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

Frequently asked questions

What is Intransitive game in simple terms?

An intransitive or non-transitive game is a zero-sum game in which pairwise competitions between the strategies contain a cycle. If strategy A beats strategy B, B beats C, and C beats A, then the binary relation "to beat" is intransitive, since transitivity would require that A beat C.

Why does Intransitive game matter?

Because it connects several mathematics 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 Intransitive 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 Intransitive game.

Tags

  • Applied mathematics stubs
  • Zero-sum games

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