Game Theory

9.

Mechanism Design and Implementation

9.1.

Social Choice Theory

9.1.1.

Social Choice Functions

9.1.2.

Arrow's Impossibility Theorem

9.1.3.

Gibbard-Satterthwaite Theorem

9.2.

Mechanism Design Fundamentals

9.2.1.

Direct vs. Indirect Mechanisms

9.2.2.

Revelation Principle

9.2.3.

Incentive Compatibility

9.2.3.1.

Dominant Strategy Implementation

9.2.3.2.

Bayesian Implementation

9.2.4.

Individual Rationality

9.2.5.

9.3.

9.3.1.

Private Value Auctions

9.3.1.1.

Independent Private Values

9.3.1.2.

First-Price Sealed-Bid

9.3.1.3.

Second-Price Sealed-Bid

9.3.1.4.

English Auction

9.3.1.5.

9.3.2.

Common Value Auctions

9.3.2.1.

9.3.2.2.

Information Aggregation

9.3.3.

Revenue Equivalence

9.3.3.1.

Theorem Statement

9.3.3.2.

Conditions and Assumptions

9.3.3.3.

Implications for Auction Design

9.3.4.

Optimal Auctions

9.3.4.1.

Revenue Maximization

9.3.4.2.

9.3.4.3.

Myerson's Optimal Auction

9.4.

Implementation Theory

9.4.1.

Nash Implementation

9.4.2.

Subgame Perfect Implementation

9.4.3.

Virtual Implementation

9.4.4.

Robust Mechanism Design

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10. Evolutionary Game Theory