arxiv: 2603.20683 · v3 · submitted 2026-03-21 · 💰 econ.TH

Recognition: 2 theorem links

· Lean Theorem

Distribution-Free Equilibrium in Search Contests

Emre Ozdenoren , Murat Erkurt

Authors on Pith no claims yet

Pith reviewed 2026-05-15 07:38 UTC · model grok-4.3

classification 💰 econ.TH

keywords search contestdistribution-free equilibriumrent dissipationsequential searchsymmetric equilibriumcontest designprize efficiency

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The pith

In search contests with sequential draws, equilibrium acceptance rates, costs, and payoffs are independent of the value distribution.

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

Players draw values one by one from an unknown distribution at a fixed cost per draw and cannot recall earlier draws; the player with the highest accepted draw wins a prize. The paper shows that the unique symmetric equilibrium produces an acceptance probability, expected total search cost per player, and expected payoff that remain exactly the same no matter what the distribution is. Aggregate search spending across all players exactly equals the prize value, so rents are fully dissipated. These invariance properties continue to hold when there are multiple prizes or when contest designers compete in a hierarchy. The size of the prize that aligns private incentives with social efficiency does depend on the distribution, however, and larger prizes are required when values are heavy-tailed.

Core claim

In the unique symmetric equilibrium, players use threshold strategies whose resulting acceptance probability, expected search expenditure, and expected payoffs are invariant to the underlying distribution of values, and the total search costs incurred by all players exactly equal the prize, producing full rent dissipation.

What carries the argument

Symmetric Nash equilibrium threshold strategy in sequential search without recall, where the distribution terms cancel in the indifference condition that determines the threshold.

If this is right

Full rent dissipation holds for any distribution.
The socially efficient prize level is larger for heavy-tailed distributions.
With a finite number of draws allowed, increasing the number of competitors can raise the quality threshold when search costs are low.
A social planner who chooses both prize and number of players prefers the smallest field size with unlimited draws unless the distribution is heavy-tailed or draws are capped.

Where Pith is reading between the lines

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

Contest designers can set prizes and field sizes without precise knowledge of the value distribution for many equilibrium properties.
The invariance result suggests similar distribution-free behavior may appear in related models of competitive information acquisition.
When draws are limited, breadth from more participants can substitute for depth in a way that reverses the usual discouragement effect.

Load-bearing premise

Players know the prize and per-draw cost, share common knowledge of the rules, and can compute and play the unique symmetric equilibrium strategy even though the distribution itself is unknown.

What would settle it

Run the game with two different distributions while holding prize and cost fixed and test whether the observed frequency with which players accept a draw stays constant.

Figures

Figures reproduced from arXiv: 2603.20683 by Emre Ozdenoren, Murat Erkurt.

read the original abstract

We study a contest in which $N$ players sequentially draw from a distribution as many times as they want at a fixed cost per draw, with no recall, and the highest accepted value wins a prize. In the unique symmetric equilibrium, the acceptance probability, expected search cost, and players' payoffs do not depend on the underlying distribution. Total search expenditure equals the prize (full rent dissipation). These distribution-free equilibrium properties extend to multiple prizes and to hierarchical competition among designers. The efficient prize that aligns competitive incentives with the social optimum is distribution-dependent: heavy-tailed distributions require much larger prizes. With finite number of draws, adding competitors can raise the quality threshold when search costs are low, reversing the discouragement of the unlimited-draw case. A planner choosing both the prize and the field size always prefers the minimum field ($N=2$) with unlimited draws, but heavy-tailed distributions and finitely many draws favor larger fields, as breadth of parallel exploration compensates for limited depth of individual search.

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

0 major / 3 minor

Summary. The paper models a search contest with N players sequentially drawing values from an unknown distribution F at fixed cost c per draw (no recall), where the highest accepted value wins prize v. It claims that in the unique symmetric equilibrium the acceptance probability, expected search cost, and payoffs are independent of F, with full rent dissipation (aggregate search expenditure equals v). These distribution-free properties extend to multiple prizes and hierarchical competition among designers. The socially efficient prize is F-dependent (larger for heavy-tailed distributions), finite-draw cases can reverse the usual discouragement effect when costs are low, and a planner prefers N=2 with unlimited draws except under heavy tails or finite draws.

Significance. If the central claims hold, the distribution-free equilibrium properties represent a clean and robust contribution to contest and search theory, showing that equilibrium behavior and dissipation are invariant to F under standard assumptions. This simplifies analysis and yields testable predictions without needing to specify F. The extensions to multiple prizes, the F-dependent efficient prize, and the finite-draw reversal of competition effects add substantive value for mechanism design in R&D or labor-market contests. The model ships parameter-free equilibrium characterizations and falsifiable predictions, which strengthen its assessment.

minor comments (3)

[Abstract] Abstract: the statement that 'the efficient prize ... is distribution-dependent' could briefly note the direction of dependence (e.g., larger for heavy tails) to improve immediate readability.
[Section 2] Notation: ensure the common-knowledge assumption on the game rules and the fact that F is known up to its family (but not parameters) is stated explicitly when first introducing the equilibrium strategy in the main text.
[Section 5] The finite-draw extension would benefit from a small numerical table illustrating the threshold reversal for low c and different N to make the contrast with the unlimited-draw case concrete.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our paper and the recommendation for minor revision. The referee's summary accurately captures the central results on distribution-free equilibrium properties, full rent dissipation, and the extensions to multiple prizes, hierarchical competition, efficient prize design, and finite-draw cases.

Circularity Check

0 steps flagged

Derivation self-contained from equilibrium indifference conditions

full rationale

The paper derives its distribution-free equilibrium properties (acceptance probability, expected search cost, payoffs independent of F, and full rent dissipation) directly from the symmetric Nash equilibrium conditions in the sequential search model. The indifference between accepting and continuing search produces equations in which the distribution F cancels out when computing the expected value of the next draw and the continuation value, without any fitted parameters, self-citation chains, or imported uniqueness theorems. The full rent dissipation result follows immediately from the equilibrium payoff equaling the expected marginal search cost under the prize value. No load-bearing step reduces to a prior result by construction or renames an empirical pattern; the claims are obtained by solving the model under standard assumptions on F and common knowledge of the rules.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard assumptions from game theory and optimal search theory with no new free parameters, invented entities, or ad-hoc axioms introduced beyond the model primitives.

axioms (2)

domain assumption Players are risk-neutral expected-payoff maximizers with common knowledge of the game structure, prize, and cost.
Standard assumption enabling symmetric equilibrium analysis in contest models.
domain assumption The value distribution is fixed and known in form but the equilibrium strategies adjust thresholds accordingly.
Required for the claimed distribution independence to hold via reservation-value logic.

pith-pipeline@v0.9.0 · 5462 in / 1385 out tokens · 71296 ms · 2026-05-15T07:38:57.413163+00:00 · methodology

discussion (0)

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 echoes

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echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

In the unique symmetric equilibrium, the acceptance probability, expected search cost, and players' payoffs do not depend on the underlying distribution. Total search expenditure equals the prize (full rent dissipation).
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction echoes

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echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

the equilibrium acceptance quantile depends only on the number of players, the search depth, and the cost-prize ratio, not on the underlying distribution

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
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

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