Mechanism design in the context of "Gibbard's theorem"

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⭐ Core Definition: Mechanism design

Mechanism design (sometimes implementation theory or institution design) is a branch of economics and game theory. It studies how to construct rules—called mechanisms or institutions—that produce good outcomes according to some predefined metric, even when the designer does not know the players' true preferences or what information they have. Mechanism design thus focuses on the study of solution concepts for a class of private-information games.

Mechanism design has broad applications, including traditional domains of economics such as market design, but also political science (through voting theory). It is a foundational component in the operation of the internet, being used in networked systems (such as inter-domain routing), e-commerce, and advertisement auctions by Facebook and Google.

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👉 Mechanism design in the context of Gibbard's theorem

In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. It states that for any deterministic process of collective decision, at least one of the following three properties must hold:

  1. The process is dictatorial, i.e. there is a single voter whose vote chooses the outcome.
  2. The process limits the possible outcomes to two options only.
  3. The process is not straightforward; the optimal ballot for a voter "requires strategic voting", i.e. it depends on their beliefs about other voters' ballots.

A corollary of this theorem is the Gibbard–Satterthwaite theorem about voting rules. The key difference between the two theorems is that Gibbard–Satterthwaite applies only to ranked voting. Because of its broader scope, Gibbard's theorem makes no claim about whether voters need to reverse their ranking of candidates, only that their optimal ballots depend on the other voters' ballots.

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Mechanism design in the context of Social choice theory

Social choice theory is a branch of welfare economics that extends the theory of rational choice to collective decision-making. Social choice studies the behavior of different mathematical procedures (social welfare functions) used to combine individual preferences into a coherent whole. It contrasts with political science in that it is a normative field that studies how a society can make good decisions, whereas political science is a descriptive field that observes how societies actually do make decisions. While social choice began as a branch of economics and decision theory, it has since received substantial contributions from mathematics, philosophy, political science, and game theory.

Real-world examples of social choice rules include constitutions and parliamentary procedures for voting on laws, as well as electoral systems; as such, the field is occasionally called voting theory. It is closely related to mechanism design, which uses game theory to model social choice with imperfect information and self-interested citizens.

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Mechanism design in the context of Information asymmetry

In contract theory, mechanism design, and economics, an information asymmetry is a situation where one party has more or better information than the other.

Information asymmetry creates an imbalance of power in transactions, which can sometimes cause the transactions to be inefficient, causing market failure in the worst case. Examples of this problem are adverse selection, moral hazard, and monopolies of knowledge.

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LINKED FROM (PARENTS)
← Social choice theory ← Information asymmetry ← Gibbard's theorem
LINKS TO (CHILDREN)
Social choice → Economics → Game theory → Game form → Social welfare function → Solution concept → Market design → Political science → Voting theory → Internet → Inter-domain routing → E-commerce → Sponsored search auction → Facebook → Google →