FA-12716 / Auction allocation rules / Open access

One bidder wins two mutually exclusive package offers · case 01

One bidder wins two mutually exclusive package offers.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Item disjointness is checked without bidder exclusivity.

VERIFIED REPAIR

Implement the stated toy allocation contract directly: Process [bidder, item-list, value] offers by descending value, stable on ties. Accept only if its bidder has not won and none of its items are used. Return accepted original indices. This is a greedy policy, not optimal welfare.

Unsuccessful approach: Keeping only the first bid per bidder before ranking throws away their higher priority offer.

Case contract

Process [bidder, item-list, value] offers by descending value, stable on ties. Accept only if its bidder has not won and none of its items are used. Return accepted original indices. This is a greedy policy, not optimal welfare.

Why this case matters

Deterministic teaching model for reviewing auction allocation software; not a representation of any venue or financial advice.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(offers):
    used=set(); result=[]
    for i,(owner,items,value) in sorted(enumerate(offers),key=lambda x:-x[1][2]):
     if not used.intersection(items): result.append(i); used.update(items)
    return result
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('later better exclusive offer', solve([['a',['x'],2],['a',['y'],10+N],['b',['x'],3]]), [1,2])
check('disjoint same bidder', solve([['a',['x'],9],['a',['y'],8]]), [0])
check('overlapping items', solve([['a',['x'],9],['b',['x'],8]]), [0])
check('different owners disjoint', solve([['a',['x'],9],['b',['y'],8]]), [0,1])
check('stable ties', solve([['a',['x'],8],['b',['x'],8]]), [0])
check('no offers', solve([]), [])
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
later better exclusive offer	`[1, 2]`	`[1, 2]`	Passed
disjoint same bidder	`[0, 1]`	`[0]`	Failed
overlapping items	`[0]`	`[0]`	Passed
different owners disjoint	`[0, 1]`	`[0, 1]`	Passed
stable ties	`[0]`	`[0]`	Passed
no offers	`[]`	`[]`	Passed

SHA-256 / 731ac6ff52b4fd8eb4c317eefb6ccdbca148ff68bb26bd7e752114f769b80bc8

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(offers):
    seen=set(); retained=[]
    for i,o in enumerate(offers):
     if o[0] not in seen: retained.append((i,o)); seen.add(o[0])
    used=set(); result=[]
    for i,(owner,items,value) in sorted(retained,key=lambda x:-x[1][2]):
     if not used.intersection(items): result.append(i); used.update(items)
    return result
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('later better exclusive offer', solve([['a',['x'],2],['a',['y'],10+N],['b',['x'],3]]), [1,2])
check('disjoint same bidder', solve([['a',['x'],9],['a',['y'],8]]), [0])
check('overlapping items', solve([['a',['x'],9],['b',['x'],8]]), [0])
check('different owners disjoint', solve([['a',['x'],9],['b',['y'],8]]), [0,1])
check('stable ties', solve([['a',['x'],8],['b',['x'],8]]), [0])
check('no offers', solve([]), [])
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
later better exclusive offer	`[2]`	`[1, 2]`	Failed
disjoint same bidder	`[0]`	`[0]`	Passed
overlapping items	`[0]`	`[0]`	Passed
different owners disjoint	`[0, 1]`	`[0, 1]`	Passed
stable ties	`[0]`	`[0]`	Passed
no offers	`[]`	`[]`	Passed

SHA-256 / 88582cd386f7f66f90cc1c910589ddfa784bf7f8b30e7308288d430cea83eb23

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(offers):
    used=set(); owners=set(); result=[]
    for i,(owner,items,value) in sorted(enumerate(offers),key=lambda x:-x[1][2]):
     if owner not in owners and not used.intersection(items):
      result.append(i); owners.add(owner); used.update(items)
    return result
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('later better exclusive offer', solve([['a',['x'],2],['a',['y'],10+N],['b',['x'],3]]), [1,2])
check('disjoint same bidder', solve([['a',['x'],9],['a',['y'],8]]), [0])
check('overlapping items', solve([['a',['x'],9],['b',['x'],8]]), [0])
check('different owners disjoint', solve([['a',['x'],9],['b',['y'],8]]), [0,1])
check('stable ties', solve([['a',['x'],8],['b',['x'],8]]), [0])
check('no offers', solve([]), [])
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
later better exclusive offer	`[1, 2]`	`[1, 2]`	Passed
disjoint same bidder	`[0]`	`[0]`	Passed
overlapping items	`[0]`	`[0]`	Passed
different owners disjoint	`[0, 1]`	`[0, 1]`	Passed
stable ties	`[0]`	`[0]`	Passed
no offers	`[]`	`[]`	Passed

SHA-256 / ac70d785b93568f17d14fe3b92959355224d90b468adfa0e0ed2a1d8410848db

Verification & scope

Offline toy model with explicit integer inputs; no strategic behavior or real market execution. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:38:59.439333+00:00.

Case digest / bc89b8926cc0b50a76daa6685f8cda7d72ccc248eff787386519dbe2ac79b5e8