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arxiv: 2606.01874 · v1 · pith:ZZ5SDG6Hnew · submitted 2026-06-01 · 💻 cs.GT

The Price of Decentralization in Block Building

Burak \"Oz , Fei Wu , Luis Correia , Sen Yang , Bruno Mazorra , Stefanos Leonardos This is my paper

Pith reviewed 2026-06-28 12:35 UTC · model grok-4.3

classification 💻 cs.GT
keywords block buildingdecentralizationprice of anarchypotential gameNash equilibriumutility concentrationstochastic coverage gameblockchain
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The pith

Uncoordinated builder placement in decentralized block building incurs up to a factor-2 welfare loss.

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

Builders in decentralized blockchains choose geographic regions to capture transaction fees, but placement affects overall coverage because latency decides which transactions arrive in time. The paper models this as a stochastic coverage game and shows it is an exact potential game, so a pure Nash equilibrium always exists. It proves the resulting price of anarchy is asymptotically tight at factor 2, meaning selfish location choices can reduce total coverage value by up to half relative to a coordinated planner. The same analysis yields tight concentration bounds: the lowest-utility builder earns at least half the payoff of the highest-utility builder, and the utility-share HHI stays within 12.5 percent of the egalitarian benchmark. These results measure the concrete cost of geographic decentralization for censorship resistance and fair access.

Core claim

We show that the builder region game is an exact potential game and therefore admits a pure Nash equilibrium. We prove an asymptotically tight factor-2 Price of Anarchy bound, quantifying the price of decentralization from uncoordinated builder placement, and derive tight bounds on builder utility concentration, showing that the lowest-utility builder earns at least half of the highest-utility builder's payoff, and the utility-share HHI is at most 12.5% above the egalitarian benchmark.

What carries the argument

The builder region game, a stochastic coverage game in which builders select regions, information sources emit transactions stochastically, and latency determines receipt before the deadline.

If this is right

  • Builder region choices always admit a pure Nash equilibrium.
  • Equilibrium welfare is at least half the optimal centralized welfare, with the factor-2 bound asymptotically tight.
  • The lowest-utility builder earns at least half the payoff of the highest-utility builder.
  • The utility-share HHI exceeds the egalitarian benchmark by at most 12.5 percent.

Where Pith is reading between the lines

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

  • Simulations indicate welfare losses are largest in intermediate latency regimes where peripheral sources are reachable yet selfish incentives still favor central high-value regions.
  • A planner can raise total coverage by assigning some builders to lower-payoff peripheral regions, even when this assignment differs from equilibrium utility balance.
  • Protocol designers could introduce location-weighted rewards or markets to reduce the identified price of anarchy without altering the potential-game structure.

Load-bearing premise

Latency fully determines whether each transaction is received before the deadline and information sources emit transactions stochastically over a block construction round.

What would settle it

A concrete two-region instance with fixed latencies and source values in which equilibrium total coverage falls below half the planner optimum, or in which no pure Nash equilibrium exists.

read the original abstract

Decentralized block building mechanisms replace the monopoly of a single proposer with multiple builders. However, their censorship-resistance and fair-access benefits depend not only on the number of builders, but also on whether builders are geographically positioned to provide timely transaction coverage. We study this tension between builder location choice, user transaction coverage, and reward concentration by modeling decentralized block building as a stochastic coverage game. Builders choose regions, information sources emit transactions over a block construction round, and latency determines whether each transaction is received before the deadline. We show that the builder region game is an exact potential game and therefore admits a pure Nash equilibrium. We prove an asymptotically tight factor-2 Price of Anarchy bound, quantifying the price of decentralization from uncoordinated builder placement, and derive tight bounds on builder utility concentration, showing that the lowest-utility builder earns at least half of the highest-utility builder's payoff, and the utility-share HHI is at most 12.5% above the egalitarian benchmark. We complement the theory with simulations, studying the builder region game under richer latency and source environments. We find that welfare losses are most pronounced in intermediate regimes where peripheral sources are reachable and valuable, but selfish incentives still favor regions with strong access to high-value sources. We also find that geographic and utility concentration need not align: planner allocations can improve coverage by assigning builders to lower-payoff peripheral regions, while equilibrium outcomes can be more geographically concentrated but more utility-balanced. We connect our findings to protocol design and discuss future directions on location-market modeling and alternative reward-sharing rules.

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 / 2 minor

Summary. The paper models decentralized block building as a stochastic coverage game in which builders strategically choose geographic regions, information sources emit transactions stochastically, and latency determines whether transactions are received before the block-construction deadline. It proves that the resulting builder region game is an exact potential game (hence admits a pure Nash equilibrium), establishes an asymptotically tight Price of Anarchy bound of 2, and derives tight equilibrium utility-concentration bounds (lowest-utility builder earns at least half the highest-utility builder's payoff; utility-share HHI is at most 12.5% above the egalitarian benchmark). These theoretical results are complemented by simulations under richer latency and source environments that examine welfare losses, geographic versus utility concentration, and implications for protocol design.

Significance. If the formal results hold, the work supplies a clean game-theoretic quantification of the efficiency and fairness costs of uncoordinated builder placement in decentralized block building. The exact-potential-game property, the asymptotically tight factor-2 PoA bound, and the explicit concentration inequalities are technically noteworthy strengths; the simulation findings on the misalignment between geographic and utility concentration also supply concrete guidance for protocol designers. The paper thereby contributes a rigorous foundation for location-aware mechanism design in blockchain settings.

minor comments (2)
  1. [Abstract] The abstract states the existence of proofs and simulations but does not indicate the sections or theorems in which the potential-function construction, PoA analysis, or concentration bounds appear; adding such pointers would improve readability.
  2. The model description relies on latency fully determining receipt before deadline and on stochastic emission; a brief remark on the robustness of the PoA and concentration results to small perturbations of these assumptions would strengthen the presentation.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, recognition of the technical strengths (exact potential game, asymptotically tight factor-2 PoA, and utility-concentration bounds), and recommendation of minor revision. The report accurately reflects the manuscript's contributions on modeling decentralized block building as a stochastic coverage game and the simulation insights on welfare and concentration.

Circularity Check

0 steps flagged

No significant circularity; derivations are self-contained

full rationale

The central claims rest on constructing an exact potential function for the stochastic coverage game (standard in potential-game theory), proving a factor-2 PoA bound that is shown asymptotically tight via explicit examples, and deriving min/max utility ratio ≥1/2 plus HHI bound directly from equilibrium analysis of the defined payoffs. No step reduces a prediction to a fitted parameter, invokes a self-citation as the sole justification for a uniqueness or ansatz claim, or renames an input as an output. The latency and emission model is stated as an assumption and used consistently without circular redefinition.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the modeling choice that latency gates transaction receipt and on standard potential-game theory; no free parameters or invented entities are introduced.

axioms (2)
  • domain assumption Builder region game is a stochastic coverage game in which latency determines receipt before deadline.
    Foundational modeling premise stated in the first paragraph of the abstract.
  • standard math Existence of pure Nash equilibrium follows from the game being an exact potential game.
    Invokes standard result from potential-game theory without additional proof in the abstract.

pith-pipeline@v0.9.1-grok · 5821 in / 1337 out tokens · 23452 ms · 2026-06-28T12:35:33.390915+00:00 · methodology

discussion (0)

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Reference graph

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