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arxiv: 2607.02457 · v1 · pith:Y7MESMDRnew · submitted 2026-07-02 · 💰 econ.TH

Endogenous shareholding auctions

Andrew Mackenzie , Christian Trudeau This is my paper

Pith reviewed 2026-07-03 01:45 UTC · model grok-4.3

classification 💰 econ.TH
keywords endogenous shareholding auctionsproduction economiesmonopolist demand elicitationownership sharesprofit distributionoptimal auctionsprior-free domination
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The pith

Endogenous shareholding auctions distribute a monopolist's profits to consumers according to ownership shares determined during the auction itself.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces endogenous shareholding auctions for production economies in which a monopolist must discover consumer demand to choose price and quantity. These auctions ensure that the resulting profit is shared between the monopolist and consumers based on ownership stakes that arise endogenously as the auction proceeds. The authors characterize the full class of such auctions, along with a broader class, using standard axioms, and examine which ones are optimal under prior-free domination and subjective expected welfare criteria.

Core claim

In production economies, endogenous shareholding auctions have the defining property that auction profits are distributed across the monopolist and consumers in line with ownership shares that are set over the course of the auction, and this class can be characterized by standard axioms.

What carries the argument

Endogenous shareholding auctions, in which ownership shares are determined during the auction to allocate the resulting profit.

If this is right

  • The class of endogenous shareholding auctions is fully characterized by standard axioms.
  • A larger class of auctions can also be characterized similarly.
  • Optimal auctions exist according to prior-free domination.
  • Optimal auctions exist according to subjective expected welfare.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If these auctions work as described, they could reduce the need for separate regulatory mechanisms to handle monopolist-consumer profit sharing.
  • Similar endogenous mechanisms might apply to settings where demand information must be elicited from multiple parties with conflicting interests.
  • The approach opens the possibility of auctions that self-regulate ownership in other economic contexts like resource allocation.

Load-bearing premise

The standard axioms used for characterization apply appropriately to the monopolist's demand-elicitation problem in the production economy.

What would settle it

Finding an auction that satisfies the standard axioms but fails to distribute profits exactly according to the ownership shares determined within the auction would falsify the characterization.

Figures

Figures reproduced from arXiv: 2607.02457 by Andrew Mackenzie, Christian Trudeau.

Figure 1
Figure 1. Figure 1: Myopic subsidy curve. In this example, there are four consumers. Using the quantity and price axes: (i) the known supply curve is such that S(1) = 1, S(2) = 9, S(3) = 17, and S(4) = 29, (ii) the demand curve according to the reported valuation profile v is such that Dv(1) = 30, Dv(2) = 27, Dv(3) = 22, and Dv(4) = 5, and (iii) it follows that the minimum competitive price is 17 and the maximum competitive p… view at source ↗
Figure 2
Figure 2. Figure 2: Valvular auctions and water systems. For simplicity, suppose all marginal costs are finite. Let us say that a valvular auction’s profit is the producer surplus at a minimum competitive price equilibrium, which is precisely the profit realized by the mo￾nopolist under any VCG mechanism. Imagine that initially, this quantity is represented by an unknown amount of water in an opaque profit reservoir. When the… view at source ↗
Figure 3
Figure 3. Figure 3: Proving the Invariance Lemma. In this example, there are five consumers, the supply curve is such that S(5) > S(4) = S(3) > S(2) > S(1), and p = S(4) = S(3). We want to show that the subsidy function σi is constant across V p −i ⊆ V−i : the collection of peer profiles that offer i Groves price p. The horizontal axis measures the number of peers who report more than p, the vertical axis measures the number … view at source ↗
read the original abstract

We introduce endogenous shareholding auctions for production economies where a monopolist must elicit consumer demand in order to determine price and quantity. Each of these auctions has the property that the auction's profit is distributed across the monopolist and the consumers in accordance with ownership shares that are determined over the course of the auction. We characterize this class, and a larger class, on the basis of standard axioms. Finally, we investigate optimal auctions according to both prior-free domination and subjective expected welfare.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper introduces endogenous shareholding auctions for production economies where a monopolist must elicit consumer demand to determine price and quantity. These auctions distribute the auction's profit across the monopolist and consumers according to ownership shares determined during the auction. The manuscript claims to characterize this class (and a larger class) on the basis of standard axioms and investigates optimal auctions according to prior-free domination and subjective expected welfare.

Significance. If the claimed axiomatic characterization holds and the axioms appropriately encode the incentive and feasibility constraints of the monopolist's demand-elicitation problem, the work could offer a new mechanism-design framework that endogenously links allocation, pricing, and ownership in production economies. The prior-free and subjective-welfare optimality analysis would then provide concrete guidance on mechanism selection.

major comments (1)
  1. [Abstract] Abstract: the central claim is a characterization of endogenous shareholding auctions (and a larger class) on the basis of 'standard axioms,' yet the abstract supplies neither the list of axioms nor any derivation showing that they capture incentive-compatibility, individual rationality, or feasibility constraints specific to a monopolist's demand-elicitation problem in a production economy. This omission is load-bearing because the applicability of unmodified standard axioms to the setting is unverified and directly determines whether the profit-distribution property is fully characterized.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their comments on our manuscript. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim is a characterization of endogenous shareholding auctions (and a larger class) on the basis of 'standard axioms,' yet the abstract supplies neither the list of axioms nor any derivation showing that they capture incentive-compatibility, individual rationality, or feasibility constraints specific to a monopolist's demand-elicitation problem in a production economy. This omission is load-bearing because the applicability of unmodified standard axioms to the setting is unverified and directly determines whether the profit-distribution property is fully characterized.

    Authors: The abstract is written as a concise overview of the paper's contributions, consistent with standard practice in axiomatic mechanism design. The full list of axioms, the characterization theorems, and the verification that these axioms encode the incentive-compatibility, individual-rationality, and feasibility constraints of the monopolist's demand-elicitation problem appear in Sections 3 and 4 of the manuscript (with the profit-distribution property derived directly from the axioms). We maintain that the abstract need not replicate these details, as the body of the paper supplies the required derivations and applicability checks. revision: no

Circularity Check

0 steps flagged

No circularity; characterization relies on external standard axioms

full rationale

The paper introduces endogenous shareholding auctions and states that the class (and a larger class) is characterized on the basis of standard axioms. No equations, definitions, or steps in the provided text reduce a claimed result to a fitted parameter, self-referential definition, or self-citation chain. The axioms are presented as external (standard in the field), making the derivation self-contained against independent benchmarks rather than circular by construction. This is the expected non-finding for papers whose core claims rest on cited external properties.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Review based solely on abstract; no explicit free parameters, axioms, or invented entities are detailed beyond the high-level claim of using 'standard axioms' and introducing the new auction class.

axioms (1)
  • domain assumption Standard axioms suffice to characterize the class of endogenous shareholding auctions
    The abstract states that the class is characterized on the basis of standard axioms, but does not list them.
invented entities (1)
  • Endogenous shareholding auctions no independent evidence
    purpose: Auctions in which ownership shares are determined during the auction and used to distribute the resulting profit
    The paper introduces this class as its central new object.

pith-pipeline@v0.9.1-grok · 5584 in / 1350 out tokens · 35062 ms · 2026-07-03T01:45:51.959119+00:00 · methodology

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Reference graph

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