Incentive compatibility

In game theory and economics, a mechanism is called incentive-compatible (IC)^[1]^: 415 if every participant can achieve their own best outcome by reporting their true preferences.^[1]^: 225^[2] For example, there is incentive compatibility if high-risk clients are better off in identifying themselves as high-risk to insurance firms, who only sell discounted insurance to high-risk clients. Likewise, they would be worse off if they pretend to be low-risk. Low-risk clients who pretend to be high-risk would also be worse off.^[3] The concept is attributed to the Russian-born American economist Leonid Hurwicz.^[2]

Typology

There are several different degrees of incentive-compatibility:^[4]

The stronger degree is dominant-strategy incentive-compatibility (DSIC).^[1]^: 415 It means that truth-telling is a weakly-dominant strategy, i.e. you fare best or at least not worse by being truthful, regardless of what the others do. In a DSIC mechanism, strategic considerations cannot help any agent achieve better outcomes than the truth; such mechanisms are called strategyproof,^[1]^{: 244, 752} truthful, or straightforward.
A weaker degree is Bayesian-Nash incentive-compatibility (BNIC).^[1]^: 416 It means there is a Bayesian Nash equilibrium in which all participants reveal their true preferences. In other words, if all other players act truthfully, then it is best to be truthful.^[1]^: 234

Every DSIC mechanism is also BNIC, but a BNIC mechanism may exist even if no DSIC mechanism exists.

Typical examples of DSIC mechanisms are second-price auctions and a simple majority vote between two choices. Typical examples of non-DSIC mechanisms are ranked voting with three or more alternatives (by the Gibbard–Satterthwaite theorem) or first-price auctions.

In randomized mechanisms

A randomized mechanism is a probability-distribution on deterministic mechanisms. There are two ways to define incentive-compatibility of randomized mechanisms:^[1]^{: 231–232}

The stronger definition is: a randomized mechanism is universally-incentive-compatible if every mechanism selected with positive probability is incentive-compatible (i.e. if truth-telling gives the agent an optimal value regardless of the coin-tosses of the mechanism).
The weaker definition is: a randomized mechanism is incentive-compatible-in-expectation if the game induced by expectation is incentive-compatible (i.e. if truth-telling gives the agent an optimal expected value).

Revelation principles

The revelation principle comes in two variants corresponding to the two flavors of incentive-compatibility:

The dominant-strategy revelation-principle says that every social-choice function that can be implemented in dominant-strategies can be implemented by a DSIC mechanism.
The Bayesian–Nash revelation-principle says that every social-choice function that can be implemented in Bayesian–Nash equilibrium (Bayesian game, i.e. game of incomplete information) can be implemented by a BNIC mechanism.

References

^ ^a ^b ^c ^d ^e ^f ^g Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK: Cambridge University Press. ISBN 0-521-87282-0.
^ ^a ^b "Incentive compatibility | game theory". Encyclopedia Britannica. Retrieved 2020-05-25.
^ James Jr, Harvey S. (2014). "Incentive compatibility". Britannica.
^ Jackson, Matthew (December 8, 2003). "Mechanism Theory" (PDF). Optimization and Operations Research.

[agt07-1] ^ ^a ^b ^c ^d ^e ^f ^g Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK: Cambridge University Press. ISBN 0-521-87282-0.

[eb-2] "Incentive compatibility | game theory". Encyclopedia Britannica. Retrieved 2020-05-25.

[3] James Jr, Harvey S. (2014). "Incentive compatibility". Britannica.

[4] Jackson, Matthew (December 8, 2003). "Mechanism Theory" (PDF). Optimization and Operations Research.

[1]

[2]

[3]

[4]

Topics of game theory
Definitions	Congestion game 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 Mechanism design
Equilibrium concepts	Bayes correlated equilibrium Bayesian Nash equilibrium Berge equilibrium Core Correlated equilibrium Coalition-proof Nash equilibrium Epsilon-equilibrium Evolutionarily stable strategy Gibbs equilibrium Mertens-stable equilibrium Markov perfect equilibrium Nash equilibrium Pareto efficiency Perfect Bayesian equilibrium Proper equilibrium Quantal response equilibrium Quasi-perfect equilibrium Risk dominance Satisfaction equilibrium Self-confirming equilibrium Sequential equilibrium Shapley value Strong Nash equilibrium Subgame perfection Trembling hand equilibrium
Strategies	Appeasement Backward induction Bid shading Collusion Cheap talk De-escalation Deterrence Escalation Forward induction Grim trigger Markov strategy Pairing strategy Dominant strategies Pure strategy Mixed strategy Strategy-stealing argument Tit for tat
Classes of games	Auction Bargaining problem Global game Intransitive game Mean-field game n-player game Perfect information Large Poisson game Potential game Repeated game Screening game Signaling game Strictly determined game Stochastic game Symmetric game Zero-sum game
Games	Go Chess Infinite chess Checkers All-pay auction Prisoner's dilemma Gift-exchange game Optional prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Lewis signaling game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Electronic mail 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 Bertrand competition Cournot competition Stackelberg competition Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Induction puzzles Trust game Princess and monster game Rendezvous problem
Theorems	Aumann's agreement theorem Folk theorem Minimax theorem Nash's theorem Negamax theorem Purification theorem Revelation principle Sprague–Grundy theorem Zermelo's theorem
Key figures	Albert W. Tucker Amos Tversky Antoine Augustin Cournot 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 John Conway Jean Tirole Jean-François Mertens Jennifer Tour Chayes John Harsanyi John Maynard Smith 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
Search optimizations	Alpha–beta pruning Aspiration window Principal variation search max^n algorithm Paranoid algorithm Lazy SMP
Miscellaneous	Bounded rationality Combinatorial game theory Confrontation analysis Coopetition Evolutionary game theory Glossary of game theory List of game theorists List of games in game theory No-win situation Topological game Tragedy of the commons

Fahrer / Team für die Suche eingeben: