science

One-shot deviation principle

One-shot deviation principle 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 One-shot deviation principle rather than just read about it. In short: In game theory, the one-shot deviation principle (also known as the single-deviation property) is a principle used to determine whether a strategy in a sequential game constitutes a subgame perfect equilibrium. An SPE is a Nash equilibrium where no player has an incentive to deviate in any subgame.

Key takeaways

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

Reference excerpt

In game theory, the one-shot deviation principle (also known as the single-deviation property) is a principle used to determine whether a strategy in a sequential game constitutes a subgame perfect equilibrium. An SPE is a Nash equilibrium where no player has an incentive to deviate in any subgame. It is closely related to the principle of optimality in dynamic programming. The one-shot deviation principle states that a strategy profile of a finite multi-stage extensive-form game with observed actions is an SPE if and only if there exist no profitable single deviation for each subgame and every player. In simpler terms, if no player can profit (increase their expected payoff) by deviating from their original strategy via a single action (in just one stage of the game), then the strategy profile is an SPE. The one-shot deviation principle is very important for infinite horizon games, in which the backward induction method typically doesn't work to find SPE. In an infinite horizon game where the discount factor is less than 1, a strategy profile is a subgame perfect equilibrium if and only if it satisfies the one-shot deviation principle.

Definitions The following is the paraphrased definition from Watson (2013). To check whether strategy s is a subgame perfect Nash equilibrium, we have to ask every player i and every subgame, if considering s, there is a strategy s’ that yields a strictly higher payoff for player i than does s in the subgame. In a finite multi-stage game with observed actions, this analysis is equivalent to looking at single deviations from s, meaning s’ differs from s at only one information set (in a single stage). Note that the choices associated with s and s’ are the same at all nodes that are successors of nodes in the information set where s and s’ prescribe different actions.

Example Consider a symmetric game with two players in which each player makes binary choice decisions, A or B, in each of three stages. In each stage, the players observe the choices made in the previous stages (if any). Note that each player has 21 information sets, one in the first stage, four in the second stage (because players observe the outcome of the first stage, one of four action combinations), and 16 in the third stage (4 times 4 histories of action combinations from the first two stages). The single-deviation condition requires checking each of these information sets, asking in each case whether the expected payoff of the player on the move would strictly increase by deviating at only this information set.

References

Worked examples

Example 1 — a first encounter with One-shot deviation principle

Start with the simplest possible case. Write down what One-shot deviation principle 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 One-shot deviation principle 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 One-shot deviation principle 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 One-shot deviation principle

In research: One-shot deviation principle 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 One-shot deviation principle 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: One-shot deviation principle is common in secondary-school and first-year university syllabi. It links to neighbouring topics Game theory, so understanding it makes those chapters shorter.
In everyday life: Look for One-shot deviation principle 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 One-shot deviation principle in 20 minutes

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

Frequently asked questions

What is One-shot deviation principle in simple terms?

Why does One-shot deviation principle 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 One-shot deviation principle?

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 One-shot deviation principle.