Implementation theory is an area of research in

game theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...

concerned with whether a class of mechanisms (or institutions) can be designed whose equilibrium outcomes implement a given set of

normative Normativity is the phenomenon in human societies of designating some actions or outcomes as good, desirable, or permissible, and others as bad, undesirable, or impermissible. A Norm (philosophy), norm in this sense means a standard for evaluatin ...

goals or

welfare Welfare may refer to: Philosophy *Well-being (happiness, prosperity, or flourishing) of a person or group * Utility in utilitarianism * Value in value theory Economics * Utility, a general term for individual well-being in economics and decision ...

criteria.Palfrey, Thomas R. "Chapter 61 Implementation Theory." Handbook of Game Theory with Economic Applications, 2002. . There are two general types of implementation problems: the economic problem of producing and allocating

public In public relations and communication science, publics are groups of individual people, and the public (a.k.a. the general public) is the totality of such groupings. This is a different concept to the sociology, sociological concept of the ''Öf ...

and

private good Private or privates may refer to: Music * "In Private", by Dusty Springfield from the 1990 album ''Reputation'' * Private (band), a Denmark-based band * "Private" (Ryōko Hirosue song), from the 1999 album ''Private'', written and also recorded ...

s and choosing over a finite set of alternatives.Maskin, Eric and Sjöström, Tomas. "Implementation Theory." Handbook of Social Choice and Welfare, 2002. . In the case of producing and allocating public/private goods,

solution concept In game theory, a solution concept is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The most comm ...

s are focused on finding dominant strategies. In his paper "Counterspeculation, Auctions, and Competitive Sealed Tenders",

William Vickrey William Spencer Vickrey (21 June 1914 – 11 October 1996) was a Canadian-American professor of economics and Nobel Laureate. He was a lifelong faculty member at Columbia University. A theorist who worked on public economics and mechanism design, ...

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 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 i ...

rule is dominant strategy

incentive compatible In game theory and economics, a mechanism is called incentive-compatible (IC) if every participant can achieve their own best outcome by reporting their true preferences. For example, there is incentive compatibility if high-risk clients are bette ...

, or

strategy-proof In mechanism design, a strategyproof (SP) mechanism is a game form in which each player has a weakly- dominant strategy, so that no player can gain by "spying" over the other players to know what they are going to play. When the players have privat ...

, if the associated

revelation mechanism The revelation principle is a fundamental result in mechanism design, social choice theory, and game theory which shows it is always possible to design a strategy-resistant implementation of a social decision-making mechanism (such as an elector ...

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

rules may be impossible to implement under specific game conditions.

Implementability

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 Game form, mechanisms or institutions—that produce good outcomes according to Social ...

, implementability is a property of a

social choice function In welfare economics and social choice theory, a social welfare function—also called a social ordering, ranking, utility, or choice function—is a function that ranks a set of social states by their desirability. Each person's preferences ...

. It means that there is an

incentive-compatible In game theory and economics, a mechanism is called incentive-compatible (IC) if every participant can achieve their own best outcome by reporting their true preferences. For example, there is incentive compatibility if high-risk clients are bette ...

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 In mechanism design, a strategyproof (SP) mechanism is a game form in which each player has a weakly-dominant strategy, so that no player can gain by "spying" over the other players to know what they are going to play. When the players have private ...

). * 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.Martin J. Osborne & Ariel Rubinstein: A Course in Game Theory (1994).

References

{{game theory Game theory

Implementability

See also

References