Mechanism Design (Book)

- mechanism design - resource allocation design of the system and incentive - Toyotaka Sakai , Yuji Fujinaka , Takuma Wakayama (2008)

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The 2007 Nobel Prize in Economics was awarded to Leonid Hurwitz, Eric Maskin, and Roger Myerson for “fundamental contributions to mechanism design theory.

• Maskin’s theorem

• Definition of Strategic Resistance

• Correspondence with theory of games (→)

• Each individual $i\in I$ has a set of messages ${\mathcal{D}}_i$ (→ preference space)

• Each individual strategically chooses a message ${\succsim }_i\in {\mathcal{D}}_i$(→preference)

• The function $f$ that gives the consequence determines the consequence of the game [$ f(\succsim)\in X

• Counter-strategy is the ruling strategic equilibrium of the true preference group itself in this game.

  • direct game : $(\succsim ,\mathcal{D},f)$
  • direct mechanism : $(\mathcal{D},f)$

No distinction is made between the ideal to be realized (social choice function) and the method used to guide it (direct mechanism).

• I would like to distinguish this
• Also, ruling strategy equilibrium is a kind of open concept, but it is difficult to handle, so I would like to extend it to handle general solution concepts.

Set of messages $M_i$ Pair of messages $m\equiv (m_1,m_2,\dots ,m_n)\in M_I\equiv M_1\times M_2\times \cdots \times M_n$ Function to choose a consequent for a pair of messages (consequent function) $g:M_I\to X$. $M\equiv (M_i{)}_{i\in I}$ Mechanism (indirect mechanism): $(M,g)$Definition of mechanism Direct mechanism: $M_i={\mathcal{D}}_i,g=f$ Game $(\succsim ,M,q)]fortruepreferencepair[$ \succsim \in \mathscr{D}_I$ Mechanisms are generators that give games to each true preference. mechanism Think of the corresponding S that is as open concept of the game

• $S(\cdot ,M,g):{\mathcal{D}}_I\twoheadrightarrow M_I$

$g(S(\succsim ,M,g))\equiv \{x\in X:\exists m\in S(\succsim ,M,g),x=g(m)\}=F(\succsim )$

• non-repudiability
• If Gian, with the help of Dekisugi’s suggestion, says, “Let’s all share Suneo’s New Year’s money equally!” Nobita has no reason to oppose it.
• Suneo can’t refuse to object alone.
• Bayesian incentive compatibility

Table of Contents Chapter 1 SOCIAL CHOICE and its execution

• 1.1 Introduction - King Solomon’s dilemma - Glaser-Marmanism
• 1.2 Basic Concepts
  • 1.2.1 Social Choice Response and Execution Mechanism
  • 1.2.2 Concept of Mechanism Design
• 1.3 Nash Execution and Maskin’s theorem
  • 1.3.1 Definitions
  • 1.3.2 Maskin’s theorem
  • 1.3.3 Criticisms of the Maskin Mechanism and Nash Execution
  • 1.3.4 General Feasibility and Individual Mechanism Design
• 1.4 strategicity
  • 1.4.1 Domination Strategy Execution and Strategy Resistance
  • 1.4.2 Non-domination strategy implementation and strategy resistance
  • 1.4.3 Nash Execution and Coalition Tolerance

Chapter 2 public decision-making.

• 2.1 Introduction
• 2.2 Voting Environment
  • 2.2.1 Gibert-Saththwaite theorem
  • 2.2.2 Domain Expansion
  • 2.2.3 Domain Reduction
• 2.3 Probabilistic environment
  • 2.3.1 Substantial Execution
  • 2.3.2 system of random dictatorship
• 2.4 Quasi-linear environment
  • 2.4.1 Configuration
  • 2.4.2 Groves function
  • 2.4.3 expected externality function

II Application Chapter 3 exchange economy.

• 3.1 Introduction
• 3.2 Basic Settings
• 3.3 Operation of Walras Distribution and Hurwitz theorem
  • 3.3.1 Strategic Manipulation in an Exchange Economy
  • 3.3.2 Generalization of the Hurwitz Theorem
  • 3.3.3 Related Matters
• 3.4 Nash Execution
  • 3.4.1 Walras Distribution and Constraint Walras Distribution
  • 3.4.2 Execution Mechanisms for Constraint Warlas Response

Chapter 4 Auction

• 4.1 Introduction
• 4.2 Basic Settings
• 4.3 Auction rules, strategies, and their synthesis
  • 4.3.1 Auction Rules
  • 4.3.2 Strategies
  • 4.3.3 Synthesis of Auction Rules and Strategies
• 4.4 Auction Objectives
• 4.5 Efficient Auction
  • 4.5.1 Second Price Auction second-price auction
  • 4.5.2 First Price Auction
• 4.6 income equivalence theorem and Optimal Auction
  • 4.6.1 Setup
  • 4.6.2 Income equivalence theorem
  • 4.6.3 Optimal Auction

Chapter 5 fair share.

• 5.1 Introduction
• 5.2 Basic Settings
  • 5.2.1 Model
  • 5.2.2 Nature and Axioms of Resource Allocation
• 5.3 Strategic Resistance
  • 5.3.1 Impossibility Theorem
  • 5.3.2 Possibility theorem
• 5.4 Nash Execution Potential

Chapter 6 non-dividend goods exchange.

• 6.1 Introduction
• 6.2 Basic Settings
• 6.3 Top Trading Cycle Algorithm
• 6.4 Executability of Strong Core Core (Game Theory).
• 6.5 Application to renal transplant matching

Chapter 7 matching.

• 7.1 Introduction
• 7.2 Basic Settings
• 7.3 Gale-Chapleau algorithm
• 7.4 One-sided dominance strategy
• 7.5 Bilateral Domination Strategies
• 7.6 Maskin Monotonic Response
• 7.7 Basic Settings for Many-to-One Matching
• 7.8 Treatment of ≿b in many-to-one matching and basic results
  • 7.8.1 ≿b as an order derived from extended preferences
  • 7.8.2 ≿b as a priority
• 7.9 Boston Method

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