Implementation theory is an area of research in

game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...

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

normative Normative generally means relating to an evaluative standard. 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 in ...

goals or

welfare Welfare, or commonly social welfare, is a type of government support intended to ensure that members of a society can meet basic human needs such as food and shelter. Social security may either be synonymous with welfare, or refer specificall ...

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 sociological concept of the ''Öffentlichkei ...

and

private goods A private good is defined in economics as "an item that yields positive benefits to people" that is excludable, i.e. its owners can exercise private property rights, preventing those who have not paid for it from using the good or consuming its be ...

and choosing over a finite set of alternatives.Maskin, Eric. "Implementation Theory." Handbook of Social Choice and Welfare, 2002. . 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 William Spencer Vickrey (21 June 1914 – 11 October 1996) was a Canadian-American professor of economics and Nobel Laureate. Vickrey was awarded the 1996 Nobel Memorial Prize in Economic Sciences with James Mirrlees for their research into the e ...

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 or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a ''collective decision'' or ''social welfare'' in some sense.Amartya Sen (2008). "Soci ...

rule is dominant strategy

incentive compatible A mechanism is called incentive-compatible (IC) if every participant can achieve the best outcome to themselves just by acting according to their true preferences. There are several different degrees of incentive-compatibility: * The stronger d ...

, or

strategy-proof In game theory, an asymmetric game where players have private information is said to be strategy-proof or strategyproof (SP) if it is a weakly-dominant strategy for every player to reveal his/her private information, i.e. given no information abou ...

, if the associated

revelation mechanism The revelation principle is a fundamental principle in mechanism design. It states that if a social choice function can be implemented by an arbitrary mechanism (i.e. if that mechanism has an equilibrium outcome that corresponds to the outcome of ...

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.Jackson, Matthew O. "A Crash Course in Implementation Theory." Social Choice and Welfare 18, no. 4 (2001): 655–708. . . Although largely theoretical, implementation theory may have profound implications on policy creation because some

rules may be impossible to implement under specific game conditions.

References

{{game theory Game theory