Pith Number

pith:Q3KXPZCF

pith:2025:Q3KXPZCFTNEEEPYBZPLSDTXJEQ

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How to sell a service with uncertain outcomes

Alec Sun, Haifeng Xu, Krishnamurthy Iyer, You Zu

Sellers maximize profit for uncertain-outcome services only with two-stage contracts combining upfront and usage payments.

arxiv:2502.13334 v2 · 2025-02-18 · cs.GT

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\pithnumber{Q3KXPZCFTNEEEPYBZPLSDTXJEQ}

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We show that this two-stage payment structure is necessary to maximize profit: only upfront prices or only usage prices is insufficient. [...] we derive a fully-polynomial time approximation scheme (FPTAS) for the maximum profit for a constant number of buyer types. Finally, we prove that in the single-parameter setting [...] seller revenue can be maximized using a menu consisting of a single contract.

C2weakest assumption

The model assumes the seller has the ability to commit to an action and the buyer is free to accept or reject the outcome after seeing its realized quality (core setup stated in the abstract).

C3one line summary

Models selling uncertain-outcome services via two-stage contracts, proves the structure is necessary for max profit, gives FPTAS for constant buyer types, and shows single-contract optimality in single-parameter settings.

Receipt and verification

First computed	2026-06-25T00:18:10.928628Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86d577e4459b48423f01cbd721cee9242eb0dc3fcd58cd31a215ee186e75d76c

Aliases

arxiv: 2502.13334 · arxiv_version: 2502.13334v2 · doi: 10.48550/arxiv.2502.13334 · pith_short_12: Q3KXPZCFTNEE · pith_short_16: Q3KXPZCFTNEEEPYB · pith_short_8: Q3KXPZCF

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Q3KXPZCFTNEEEPYBZPLSDTXJEQ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 86d577e4459b48423f01cbd721cee9242eb0dc3fcd58cd31a215ee186e75d76c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f23df5ebeb1d15ae98daefec92517c21a11eae46ae6d6b7f936fc4fa7817fb0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2025-02-18T23:28:30Z",
    "title_canon_sha256": "465e4e1380ae2bb0d17f5b0c859bc91cd2f028275d1efd4e760e27073285c670"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.13334",
    "kind": "arxiv",
    "version": 2
  }
}