Mechanism Design (Book)
https://gyazo.com/b3945c4e4d3b89b02283d87bb8e80629
mechanism design - resource allocation design of the system and incentive
Toyotaka Sakai , Yuji Fujinaka , Takuma Wakayama (2008)
Amazon
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 (→<correspondence source concept>)
Each individual $ i \in I has a set of messages $ \mathscr{D}_i (→ preference space)
Each individual strategically chooses a message $ \succsim_i \in \mathscr{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, \mathscr{D}, f)
direct mechanism : $ (\mathscr{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, \ldots, 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 = \mathscr{D}_i, g = f
Game $ (\succsim, M, q)] for true preference pair [$ \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) : \mathscr{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)
https://gyazo.com/fef969317b35be72e7755f6858d42463
https://gyazo.com/e9e1076b3684c08b04ec2921669890b3
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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