Mechanism Design

VCG, auction formats, matching, voting — designing the rules of the game.
TUTORIALS

Mechanism Design

VCG, auction formats, matching, voting — designing the rules of the game.

Combinatorial Auctions — Bidding on Bundles of Items

mechanism-design
combinatorial-auctions
integer-programming

Implement the winner determination problem for combinatorial auctions using integer programming with lpSolve, model a spectrum auction with complementarities, compare VCG and first-price payment rules, and demonstrate the exposure problem in R.

May 8, 2026

Deferred acceptance — stable matching via the Gale-Shapley algorithm

mechanism-design
stable-matching
gale-shapley
market-design

Implement the Gale-Shapley deferred acceptance algorithm for stable matching in R, prove proposer-optimality and strategy-proofness, simulate matching quality across problem sizes, and visualize the lattice of stable matchings.

May 8, 2026

Practical Matching Market Design: From NRMP to School Choice

mechanism-design
matching-markets

Implement the Gale-Shapley deferred acceptance algorithm for many-to-one matching, simulate the National Resident Matching Program, and compare with Top Trading Cycles for school choice.

May 8, 2026

Introduction to mechanism design — engineering incentives in strategic environments

mechanism-design
revelation-principle
gibbard-satterthwaite
implementation-theory

Survey the foundations of mechanism design as ‘reverse game theory,’ covering the revelation principle, Gibbard-Satterthwaite impossibility, and implementation theory, with a worked R implementation of the pivotal mechanism for public goods provision.

May 8, 2026

The VCG mechanism — optimal multi-item allocation with truthful bidding

mechanism-design
vcg
combinatorial-auctions
incentive-compatibility

Implement the Vickrey-Clarke-Groves mechanism for combinatorial allocation in R, prove dominant-strategy incentive compatibility and allocative efficiency, compute Clarke pivot payments, and compare to sequential auctions.

May 8, 2026

The Vickrey (second-price) auction — truth-telling as a dominant strategy

mechanism-design
auctions
vickrey
dominant-strategy

Analyse the Vickrey sealed-bid second-price auction in R, prove that truthful bidding is a weakly dominant strategy, simulate revenue comparisons with first-price auctions, and visualize bidding equilibria.

May 8, 2026
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