01 Week 1
#vcg #Auction #Game_Theory
Context
The long term objective is to understand and simulate VCG auction mechanism for different resource allocation problems.
Mechanism design plays a central role in efficient allocation. Understanding first-price, second-price and VCG auctions helps to form the theoretical foundation before moving to more applied resource sharing models.
My medium term goal:
- Develop a simulation capable of modeling a dynamic resource allocation under different auction schemes.
- Validate theoretical predictions computationally
- Extend towards spectrum-sharing models
What I Did
Theoretical Study
Reviewed Lecture Material on
- First price auctions
- Second Price Auctions
- VCG Mechanism
Understood:
- Incentive compatibility in VCG
- Dominant strategy property
- Revenue equivalence intuition
- Difference between allocation rule and payment rule
Computational Work
- Studied SciPy documentation
- Implemented a small scale VCG simulation using SimPy for Discrete Event Simulation
- Logged Bids, Order Statistics , Payments, Utilities
- Verified Results Empirically
Insights
VCG payment formula becomes much clearer when implemented as : remove bidder i -> recompute welfare -> compute externality
Incentives vs revenue are separate dimensions - Truthful bidding maximizes incentive compatibility but not necessarily maximize revenue.
Simulation infrastructure is reusable. The current framework can be extended to multi item VCG, spectrum allocation etc.
Agenda for Next week
- Read article “The VCG Auction in Theory and Practice” by Hal R. Varian and Christopher Harris
- Extract model definition, assumptions ,allocation and payment rules.
- Reproduce baseline model in code
- Attempt simulation of the simplest version of that model