science

Implementation theory

Implementation theory 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 Implementation theory rather than just read about it. In short: Implementation theory is an area of research in game theory concerned with whether a class of mechanisms (or institutions) can be designed whose equilibrium outcomes implement a given set of normative goals or welfare criteria. There are two general types of implementation problems: the economic problem of producing and allocating public and private goods and choosing over a finite set of alternatives.

Key takeaways

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

Reference excerpt

Implementation theory is an area of research in game theory concerned with whether a class of mechanisms (or institutions) can be designed whose equilibrium outcomes implement a given set of normative goals or welfare criteria. There are two general types of implementation problems: the economic problem of producing and allocating public and private goods and choosing over a finite set of alternatives. In the case of producing and allocating public/private goods, solution concepts are focused on finding dominant strategies. In his paper "Counterspeculation, Auctions, and Competitive Sealed Tenders", William Vickrey showed that if preferences are restricted to the case of quasi-linear utility functions then the mechanism dominant strategy is dominant-strategy implementable. "A social choice rule is dominant strategy incentive compatible, or strategy-proof, if the associated revelation mechanism has the property that honestly reporting the truth is always a dominant strategy for each agent." However, the payments to agents become large, sacrificing budget neutrality to incentive compatibility. In a game where multiple agents are to report their preferences (or their type), it may be in the best interest of some agents to lie about their preferences. This may improve their payoff, but it may not be seen as a fair outcome to other agents. Although largely theoretical, implementation theory may have profound implications on policy creation because some social choice rules may be impossible to implement under specific game conditions.

Implementability In mechanism design, implementability is a property of a social choice function. It means that there is an incentive-compatible mechanism that attains ("implements") this function. There are several degrees of implementability, corresponding to the different degrees of incentive-compatibility, including:

A function is dominant-strategy implementable if it is attainable by a mechanism which is dominant-strategy-incentive-compatible (also called strategyproof). A function is Bayesian-Nash implementable if it is attainable by a mechanism which is Bayesian-Nash-incentive-compatible. See for a recent reference. In some textbooks, the entire field of mechanism design is called implementation theory.

Worked examples

Example 1 — a first encounter with Implementation theory

Start with the simplest possible case. Write down what Implementation theory 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 Implementation theory 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 Implementation theory 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 Implementation theory

In research: Implementation theory 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 Implementation theory 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: Implementation theory 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 Implementation theory 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 Implementation theory in 20 minutes

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

Frequently asked questions

What is Implementation theory in simple terms?

Why does Implementation theory 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 Implementation theory?

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 Implementation theory.