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arxiv: 2605.19548 · v1 · pith:57PCMKKKnew · submitted 2026-05-19 · 💰 econ.TH

The Full Pareto Frontier as Kantian Equilibria

Igor Sloev , Gerasimos Lianos This is my paper

Pith reviewed 2026-05-20 02:23 UTC · model grok-4.3

classification 💰 econ.TH
keywords Kantian equilibriumPareto frontierstrategy space parametrizationsocial dilemmasPareto efficiencycooperative behaviormultiplicative equilibrium
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The pith

Any interior Pareto-efficient point can be made a Multiplicative Kantian equilibrium by shifting coordinates to impose lower bounds on actions.

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

The paper shows that the full Pareto frontier can be reached as Multiplicative Kantian equilibria simply by reparametrizing the strategy space. This reparametrization works by adding lower bounds that shift the origin of the action space. A reader would care because the result lets cooperative outcomes in social dilemmas arise from individual rationality at every efficient point, without needing to alter preferences. The argument uses a geometric alignment where the new origin sits on the common tangent to the players' indifference curves.

Core claim

For any interior Pareto-efficient point there exists a shift of coordinates imposing lower bounds on actions that makes it a Multiplicative Kantian equilibrium. The proof is constructive and relies on an intuitive geometric property: moving the origin to a point on the common tangent to players' indifference curves. This result separates the problem of efficiency from the problem of fairness, allowing any normative criterion to be implemented without loss of Pareto optimality.

What carries the argument

The geometric construction of moving the origin to a point on the common tangent to players' indifference curves.

Load-bearing premise

The strategy space can be arbitrarily reparametrized by adding lower bounds without changing the underlying preferences or the economic interpretation of the game.

What would settle it

A specific interior Pareto efficient point for which no choice of lower bounds makes the point satisfy the definition of a Multiplicative Kantian equilibrium.

read the original abstract

Multiplicative Kantian equilibrium explains cooperative behavior in social dilemmas without abandoning methodological individualism. However, its outcomes depend critically on the parametrization of the strategy space - the property of strategic non-equivalence. We investigate what fraction of the Pareto frontier can be attained by varying the strategy space. We show that the set of achievable Kantian equilibria is the entire Pareto frontier: for any interior Pareto-efficient point there exists a shift of coordinates - imposing lower bounds on actions - that makes it a Multiplicative Kantian equilibrium. The proof is constructive and relies on a intuitive geometric property: moving the origin to a point on the common tangent to players' indifference curves. This result separates the problem of efficiency from the problem of fairness, allowing any normative criterion to be implemented without loss of Pareto optimality.

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 / 2 minor

Summary. The manuscript claims that the entire Pareto frontier can be attained as Multiplicative Kantian equilibria. For any interior Pareto-efficient allocation, there exists a coordinate shift that imposes lower bounds on actions (moving the origin to a point on the common tangent to the players' indifference curves) such that the allocation becomes a Multiplicative Kantian equilibrium. The proof is constructive and geometric; the result is used to separate efficiency from fairness by showing that any normative criterion can be implemented without sacrificing Pareto optimality, despite the property of strategic non-equivalence.

Significance. If the central construction is valid, the result is significant for the theory of Kantian equilibria in social dilemmas. It shows that efficiency is not an intrinsic limitation of the equilibrium concept once the strategy space can be reparametrized, thereby allowing Kantian equilibria to support arbitrary fairness criteria while remaining Pareto efficient. The explicit geometric construction and the focus on interior points provide a clear, falsifiable existence result that directly addresses the parametrization dependence highlighted in prior work.

major comments (1)
  1. [Abstract] Abstract and the paragraph on strategic non-equivalence: the claim that the imposed lower bounds leave 'the underlying preferences or the economic interpretation of the game' unchanged is load-bearing for the separation of efficiency from fairness. The construction selects the shift purely to satisfy the common-tangent condition; the manuscript must demonstrate that these bounds have a substantive economic interpretation in the original environment rather than being an artifact of the chosen coordinates, or else the resulting Kantian equilibrium risks being coordinate-dependent in a way that undermines the normative claim.
minor comments (2)
  1. Clarify the precise definition of 'interior' Pareto-efficient point and the dimensionality of the action space assumed in the geometric argument; a brief remark on extension to n>2 players would strengthen the result.
  2. Label the common tangent and the shifted origin explicitly in any figures illustrating the construction to aid readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and positive assessment of the manuscript's significance for the theory of Kantian equilibria. We address the major comment below and indicate the revisions to be incorporated in the next version of the paper.

read point-by-point responses

  1. Referee: [Abstract] Abstract and the paragraph on strategic non-equivalence: the claim that the imposed lower bounds leave 'the underlying preferences or the economic interpretation of the game' unchanged is load-bearing for the separation of efficiency from fairness. The construction selects the shift purely to satisfy the common-tangent condition; the manuscript must demonstrate that these bounds have a substantive economic interpretation in the original environment rather than being an artifact of the chosen coordinates, or else the resulting Kantian equilibrium risks being coordinate-dependent in a way that undermines the normative claim.

    Authors: We agree that the economic interpretation of the imposed lower bounds merits further clarification to support the separation of efficiency from fairness. The coordinate shift is selected to satisfy the common-tangent condition because this geometric property directly corresponds to the equalization of marginal rates of substitution, which is the defining feature of interior Pareto efficiency. The resulting lower bounds can be interpreted substantively as redefining the baseline or status quo in the strategy space from which multiplicative deviations are evaluated under the Kantian criterion; this baseline is not arbitrary but is pinned down by the efficiency requirement itself. The reparametrization preserves the underlying preferences and the economic interpretation of the game because it is a monotonic translation of the action coordinates that leaves the feasible outcome set, the payoff functions, and the players' indifference curves over physical allocations unchanged. Strategic non-equivalence is precisely the feature that permits different choices of baseline to support different points on the frontier. We will revise the abstract and the paragraph on strategic non-equivalence to articulate this mapping explicitly and add a brief illustrative example in a standard public-goods environment showing how the shifted lower bounds correspond to economically meaningful minimum-action constraints. revision: yes

Circularity Check

0 steps flagged

Existence result via explicit coordinate-shift construction; derivation self-contained

full rationale

The central claim is an existence theorem proved by constructive reparametrization: for any interior Pareto point, a specific shift of the origin onto the common tangent is exhibited that renders the point a multiplicative Kantian equilibrium. No parameter is fitted to data, no prediction is renamed from a fit, and the load-bearing step is the geometric construction itself rather than a self-citation or definitional equivalence. The paper treats the reparametrization as preserving preferences while altering only the strategy-space origin; whether that preserves economic interpretation is a substantive modeling question, not a circularity in the derivation chain. The result is therefore independent of its inputs and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on standard properties of indifference curves and the existence of common tangents in convex preference environments. No free parameters or invented entities are introduced in the abstract description.

axioms (2)
  • domain assumption Players have convex, continuous preferences admitting well-defined indifference curves with common tangents at interior Pareto points.
    Invoked in the geometric construction that moves the origin to the common tangent point.
  • domain assumption The strategy space admits arbitrary lower-bound shifts that preserve the economic interpretation of actions.
    Required for the reparametrization to be admissible without changing the game.

pith-pipeline@v0.9.0 · 5653 in / 1319 out tokens · 24370 ms · 2026-05-20T02:23:45.184862+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    for any interior Pareto-efficient point there exists a shift of coordinates — imposing lower bounds on actions — that makes it a Multiplicative Kantian equilibrium. The proof is constructive and relies on a intuitive geometric property: moving the origin to a point on the common tangent to players' indifference curves.

  • IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Differentiating with respect to a and evaluating at a = 1 yields the necessary first-order condition for an MKE: ∂Ui(x∗)/∂x1 x1∗ + ⋯ + ∂Ui(x∗)/∂xn xn∗ = 0

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The paper appears to rely on the theorem as machinery.
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unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

  1. [1]

    Boadway, R., Marceau, N., & Mongrain , S. (2007). Redistributive taxation under ethical behaviour. Scandinavian Journal of Economics, 109(3), 505-529. De Donder, P., Llavador, H., Penczynski, S., Roemer, J. E. and Vélez Grajales, R. (2025) ‘Nash versus Kant: A game-theoretic analysis of childhood vaccination behavior’, Journal of Economics/Zeitschrift für...

    work page doi:10.1007/s00712-025- 2007

  2. [2]

    doi:10.1007/s10640-024-00867-w

    work page doi:10.1007/s10640-024-00867-w