Mechanism Design and AuctionsClass ObjectivesOutlinePresentation StyleMD in a NutshellQuestions in MDRelevance to NetworksSocial Choice TheoryArrow’s Impossibility TheoremMD DefinedSolution ConceptsImplementationTruth-telling Solution ConceptGeneral Results: Implementable Choice FunctionsVCG MechanismQuasilinear EnvironmentVCG Mechanism DefinedIntuition of VCG MechanismFeatures of VCGParticipation ConstraintApplications of Mechanism DesignPublic GoodVickery AuctionIntuition behind Vickery AuctionAuctionBasic Models of AuctionRevenue Equivalence TheoremFour Types of Traditional AuctionAscending-bid AuctionDescending-bid AuctionSealed-bid AuctionCombinatorial AuctionRecommended PapersMechanism Design and AuctionsJun ShuEECS228a, Fall 2002UC BerkeleyEE228a -- Jun Shu Mechanism Design for Networks 2Class Objectives•To introduce you to the basic concepts of mechanism design•To interest you in using mechanism design as a tool in networking research•To give you a list of references for further studyEE228a -- Jun Shu Mechanism Design for Networks 3Outline•Mechanism Design Basics•VCG Mechanism•Sample Applications•Auctions•Recommended PapersEE228a -- Jun Shu Mechanism Design for Networks 4Presentation Style•Intuition•Math•ExampleEE228a -- Jun Shu Mechanism Design for Networks 5MD in a Nutshell•Given–A set of choices–A group of people (agents) with individual preference over the choices–A group preference based on individual preference according to some rule•Ask–A planner (principal) must make a decision over the choices without knowing the individual’s preferences•Approach–Design a game for the individuals to play so that the stable outcomes (equilibriums) of the game is the decision the principal would have made had she known individual’s preferences.EE228a -- Jun Shu Mechanism Design for Networks 6Questions in MD•What kinds of “individual preferences” are possible?•What kinds of “group preferences” are possible (according to “some rules”)?•Why would an individual (the agents and the principal) want to participate in a game?•Why would an agent reveal his/her true preference to the principal?•What kinds of “stable outcomes”?EE228a -- Jun Shu Mechanism Design for Networks 7Relevance to Networks•A live network is the result of combined actions of its users and components, all of which are autonomous.•MD and Network Mapping–Agents: end-users, applications, devices, etc.–Principals: network designer, network provider, government, etc.–Outcomes: network load, network performance, network behavior•Think outside the box.•A Very New Approach.EE228a -- Jun Shu Mechanism Design for Networks 8Social Choice Theory•Preference Relation (individual)Suppose there are n agents and a set of social choices C={c1, …, cm}. The preference relation >>i over C is defined as the ordering of set C according to the preference of agent i. •Social Welfare Functional (group)A function >> that assigns a rational social preference relation, >>(>>1, …, >>n), to any profile of individual rational preference in the admissible domain.EE228a -- Jun Shu Mechanism Design for Networks 9Arrow’s Impossibility Theorem•Arrow’s Conditions–Unanimity: >> is consistent with all the unanimous decisions of the group members–Pair-wise Independent: >> over any two choices depends only on the individual preferences over these choices–Non-dictatorial: there does not exist a dictator•Arrow’s Impossibility Theorem–If |C|>2, then there is no social welfare functional that satisfies all of the above three conditions•Implication–Without any constraints, a collectivity does not behavior with the kind of coherence that we may hope from an individual. Institutional detail and procedures matter.EE228a -- Jun Shu Mechanism Design for Networks 10MD Defined•Environment: E is a triplet (N, C, U)–W.L.G., replace U with agents’ type space Θ. An agent’s utility function is ui(•,θ).•Social Choice Rule: F:U→2C•Social Choice Function: f: Θ→C •Mechanism–A mechanism M=(S1,…,Sn, g(•)) is a collection of n=|N| strategy sets (S1,…,Sn) and an outcome function g: S1x…xSn→C.–M induces a set of games, each of which has a payoff function uiM(s1,…,sn)≡ui(g(s1,…,sn)).EE228a -- Jun Shu Mechanism Design for Networks 11Solution Concepts•Solution Concept–S denotes a subset of the strategy space which produces certain kinds of unspecified equilibrium outcomes in a game induced by M under E.•Kinds of Solution Concept–Dominant Strategy Equilibrium–Bayesian Nash Equilibrium–Nash Equilibrium•Not very useful in mechanism design.EE228a -- Jun Shu Mechanism Design for Networks 12Implementation•Implementation–M S-implements F in E if, when M played, •S is not empty and ∀(s1,…,sn)∊S , g(s1,…,sn)∊F(u1,…,un) . •Weak Implementation–∃(s1,…,sn) ∊ S , g(s1,…,sn) ∊ F(u1,…,un) •Implementation of Social Choice Function•Types of Implementation–DOM-Implementation–Bayesian-Nash-ImplementationEE228a -- Jun Shu Mechanism Design for Networks 13Truth-telling Solution Concept•Direct Revelation Mechanism–A mechanism in which Si= Θi for all i and g(θ)=f(θ) for all θ ∊ Θ . •Truthful Implementation–A weak implementation is truthful if in the direct revelation mechanism, telling the truth is an equilibrium (of some sort) strategy.–Other term: incentive compatibleEE228a -- Jun Shu Mechanism Design for Networks 14General Results:Implementable Choice Functions•Good News: we can focus on the truthful implementation–Revelation Principle (Theorem)•If F is DOM-implementable in E, then there exists a weak truthful implementation in dominant strategies.•Bad News: without any constraints, little is implementable–Gibbard-Satterthwaite Impossibility TheoremIf finite |C|>2 and U includes all utility functions, only binary and dictatorial choice rules are DOM-implementable.•Constraints: a way out–Type of environment–Type of choice functions–Type of implementationEE228a -- Jun Shu Mechanism Design for Networks 15VCG Mechanism•More Restrictive Environment•DOM-ImplementationEE228a -- Jun Shu Mechanism Design for Networks 16Quasilinear Environment•n agents•C=X×Rn, each outcome is c=(x,t), where–x ∊ X is a feasible solution if Φ(x)=0; and–t ∊ Rn is a profile of transfer to the agents•U::=2Θ. Agent i’s exact utility is unknown; however it takes the
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