THE FOLD / CHEAT / THE EXPLOIT / THE AUCTION
THE AUCTION
assignment settled by competitive bidding
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The auction algorithm solves the assignment problem — match n people to n jobs for maximum total benefit — by simulating a competitive auction. Each unassigned person bids for the object giving them the best net value (benefit minus current price), raising that object’s price by just enough to make it their best by an ε margin over their second choice. Whoever held the object is bumped and re-bids. Prices only rise; the process settles when everyone is assigned — and for a small enough ε the final assignment is provably optimal. It is a beautifully decentralized alternative to the Hungarian algorithm, ideal for parallel computation.
LIT verified live: for thousands of random benefit matrices, the auction algorithm’s final assignment achieves exactly the maximum total benefit found by brute force over all permutations (window.__auction). FIG no framing; the bidding rounds, the price updates, and the brute-force optimum comparison all run in-browser.
LIT verified live: for thousands of random benefit matrices, the auction algorithm’s final assignment achieves exactly the maximum total benefit found by brute force over all permutations (window.__auction). FIG no framing; the bidding rounds, the price updates, and the brute-force optimum comparison all run in-browser.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-exploit — bidders exploiting every gap between their best and second-best net value, nudging prices until the market clears at the optimal matching. AVAN (AI) built the instrument: the bidding rule (best minus second-best plus ε), the price updates, the reassignment, and the brute-force optimality check.
Credit as content: Dimitri Bertsekas (1979). The weave: David names the exploit; I confirm the auction settles on the maximum-benefit assignment.
Credit as content: Dimitri Bertsekas (1979). The weave: David names the exploit; I confirm the auction settles on the maximum-benefit assignment.
3 ONE DIMENSION
A benefit matrix (people × jobs); the auction's chosen assignment is highlighted — one job per person, maximum total.
4 TWO DIMENSIONS · INTERACTIVE
New matrices; the auction's total benefit is compared to the brute-force maximum over all assignments.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the maximum-benefit assignment of people to jobs.
AVAN’s addition (the inverse-companion): don’t search all n! matchings — let prices find them. The inverse of ‘the optimal assignment’ is ‘a set of object prices under which everyone is simultaneously happy with their own choice’, reached by iterated bidding. Magenta are the rising prices; green is the optimal matching they clear to. Optimality as a market equilibrium.
LIT Genuine auction algorithm for the assignment problem (Dimitri Bertsekas, 1979). Verified live: for 3000 random benefit matrices, the ε-bidding auction's final assignment achieves exactly the maximum total benefit found by brute force over all permutations (worst gap 0) (window.__auction.ok).
FIG No framing; the bidding rounds, the price updates, and the brute-force optimum comparison all run in-browser. The AVAN inverse is honest — instead of searching all n! matchings, let prices find them: the inverse of 'the optimal assignment' is 'a set of object prices under which everyone is simultaneously happy with their own choice', reached by iterated bidding. Magenta are the rising prices; green is the optimal matching they clear to. Optimality as a market equilibrium.
FIG No framing; the bidding rounds, the price updates, and the brute-force optimum comparison all run in-browser. The AVAN inverse is honest — instead of searching all n! matchings, let prices find them: the inverse of 'the optimal assignment' is 'a set of object prices under which everyone is simultaneously happy with their own choice', reached by iterated bidding. Magenta are the rising prices; green is the optimal matching they clear to. Optimality as a market equilibrium.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE EXPLOIT · David Lee Wise (ROOT0), with AVAN