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Formalize regular Myerson optimality under explicit assumptions - #15

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ma-yuxuan wants to merge 8 commits into
gametheoryinlean:mainfrom
ma-yuxuan:issue-13-myerson-optimality
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Formalize regular Myerson optimality under explicit assumptions#15
ma-yuxuan wants to merge 8 commits into
gametheoryinlean:mainfrom
ma-yuxuan:issue-13-myerson-optimality

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@ma-yuxuan

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Closes #13

Summary

  • formalize the regular Myerson optimality endpoint for MSZ 12.59 under explicit analytic assumptions
  • add the reserve second-price specialization for MSZ 12.61 under common reserve assumptions
  • modularize the analytic assumption interfaces around environment, candidate/profile-split, reserve-candidate, interim measurability, and a.e. uniqueness packages
  • update the Myerson knowledge nodes to document the completed conditional endpoints and future-work boundary

Validation

  • lake build EconCSLib.MechanismDesign.Auction.OptimalSingleItem
  • lake build EconCSLib.MechanismDesign.Auction.RegularMyersonReserveSecondPrice
  • python scripts\check_knowledge_references.py docs\knowledge
  • D:\FYP\mdblueprint\.venv\Scripts\mdblueprint-check.exe docs\knowledge --lean-root .

Notes

This PR intentionally keeps primitive analytic discharge, uniform distribution examples, nonzero seller value, boundary tie-sharing variants, and non-regular ironing as follow-up work.

* `Auction.argmaxBid` - the bidder with the highest bid
* `Auction.maxBidExcluding` - the highest bid excluding a given bidder
* update lemmas for `argmaxBid` and `maxBidExcluding`

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Restructure maxBid and argmaxBid

maxBid and argmaxBid are tools based on the hypothesis "b : I -> R", which is a specialisation of single-parameter mechanism.
Define SingleParameterAuction first, then define the above tools as its methods.

BidExcluding

Bid excluding, i.e. bidProfileWithout_i should be an abstract structure in MechanismDesign, as it is helpful for the properties including DsIC.
Check what a bidProfile is, then define on it bidProfileWithout_i. The maxBidExcluding is then defined.

separate from any density-based formulas one may later derive under
independence.

## Structure hierarchy

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This hierarchy should be helpful

@zhanquen zhanquen left a comment

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Restructure firstly AuctionBasic.lean

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Formalize regular Myerson optimality under explicit analytic assumptions

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