Implementation theory

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.[1]

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.[2] 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.[3] "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."[2] 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.[4]

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.[1]

## 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.[5]

## See also

Incentive Compatibility

## References

1. ↑ 1.0 1.1 Palfrey, Thomas R. "Chapter 61 Implementation Theory." Handbook of Game Theory with Economic Applications, 2002. doi:10.1016/S1574-0005(02)03024-2.
2. ↑ 2.0 2.1 Maskin, Eric and Sjöström, Tomas. "Implementation Theory." Handbook of Social Choice and Welfare, 2002. doi:10.1016/S1574-0110(02)80009-1.
3. ↑ Vickrey, William. "Counterspeculation, Auctions, and Competitive Sealed Tenders." The Journal of Finance 16, no. 1 (1961): 8–37. doi:10.1111/j.1540-6261.1961.tb02789.x. JSTOR 2977633.
4. ↑ Jackson, Matthew O. "A Crash Course in Implementation Theory." Social Choice and Welfare 18, no. 4 (2001): 655–708. doi:10.1007/s003550100152. JSTOR 41106420.
5. ↑ Martin J. Osborne & Ariel Rubinstein: A Course in Game Theory (1994).

* v
* t
* e

Topics in game theory

Definitions|

* Cooperative game
* Determinacy
* Escalation of commitment
* Extensive-form game
* First-player and second-player win
* Game complexity
* Graphical game
* Hierarchy of beliefs
* Information set
* Normal-form game
* Preference
* Sequential game
* Simultaneous game
* Simultaneous action selection
* Solved game
* Succinct game

Equilibrium
concepts|

* Nash equilibrium
* Subgame perfection
* Mertens-stable equilibrium
* Bayesian Nash equilibrium
* Perfect Bayesian equilibrium
* Trembling hand
* Proper equilibrium
* Epsilon-equilibrium
* Correlated equilibrium
* Sequential equilibrium
* Quasi-perfect equilibrium
* Evolutionarily stable strategy
* Risk dominance
* Core
* Shapley value
* Pareto efficiency
* Gibbs equilibrium
* Quantal response equilibrium
* Self-confirming equilibrium
* Strong Nash equilibrium
* Markov perfect equilibrium

Strategies|

* Dominant strategies
* Pure strategy
* Mixed strategy
* Strategy-stealing argument
* Tit for tat
* Grim trigger
* Collusion
* Backward induction
* Forward induction
* Markov strategy

Classes
of games|

* Symmetric game
* Perfect information
* Repeated game
* Signaling game
* Screening game
* Cheap talk
* Zero-sum game
* Mechanism design
* Bargaining problem
* Stochastic game
* n-player game
* Large Poisson game
* Nontransitive game
* Global game
* Strictly determined game
* Potential game

Games|

* Go
* Chess
* Infinite chess
* Checkers
* Tic-tac-toe
* Prisoner's dilemma
* Optional prisoner's dilemma
* Traveler's dilemma
* Coordination game
* Chicken
* Centipede game
* Volunteer's dilemma
* Dollar auction
* Battle of the sexes
* Stag hunt
* Matching pennies
* Ultimatum game
* Rock paper scissors
* Pirate game
* Dictator game
* Public goods game
* Blotto game
* War of attrition
* El Farol Bar problem
* Fair division
* Fair cake-cutting
* Cournot game
* Deadlock
* Diner's dilemma
* Guess 2/3 of the average
* Kuhn poker
* Nash bargaining game
* Prisoners and hats puzzle
* Trust game
* Princess and Monster game
* Rendezvous problem

Theorems|

* Arrow's impossibility theorem
* Aumann's agreement theorem
* Folk theorem
* Minimax theorem
* Nash's theorem
* Purification theorem
* Revelation principle
* Zermelo's theorem

Key
figures|

* Albert W. Tucker
* Amos Tversky
* Ariel Rubinstein
* Claude Shannon
* Daniel Kahneman
* David K. Levine
* David M. Kreps
* Donald B. Gillies
* Drew Fudenberg
* Eric Maskin
* Harold W. Kuhn
* Herbert Simon
* Hervé Moulin
* Jean Tirole
* Jean-François Mertens
* Jennifer Tour Chayes
* John Harsanyi
* John Maynard Smith
* Antoine Augustin Cournot
* John Nash
* John von Neumann
* Kenneth Arrow
* Kenneth Binmore
* Leonid Hurwicz
* Lloyd Shapley
* Melvin Dresher
* Merrill M. Flood
* Olga Bondareva
* Oskar Morgenstern
* Paul Milgrom
* Peyton Young
* Reinhard Selten
* Robert Axelrod
* Robert Aumann
* Robert B. Wilson
* Roger Myerson
* Samuel Bowles
* Suzanne Scotchmer
* Thomas Schelling
* William Vickrey

See also|

* All-pay auction
* Alpha–beta pruning
* Bertrand paradox
* Bounded rationality
* Combinatorial game theory
* Confrontation analysis
* Coopetition
* First-move advantage in chess
* Game mechanics
* Glossary of game theory
* List of game theorists
* List of games in game theory
* No-win situation
* Solving chess
* Topological game
* Tragedy of the commons
* Tyranny of small decisions

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/Implementation theory. Read more

|

Retrieved from "https://handwiki.org/wiki/index.php?title=Implementation_theory&oldid=3989382"
*[v]: View this template
*[t]: Discuss this template
*[e]: Edit this template