Game-theoretic security under practical parameter values

Determine whether there exists a blockchain reward allocation mechanism—specifically for Proof-of-Work protocols—that can be proven game-theoretically secure under practical parameter values (such as small confirmation/finality windows), achieving formal guarantees like δ-approximate fairness and coalition-safe ε-Nash equilibrium, without requiring unrealistically large finality or eligibility window parameters as in FruitChains.

Background

The paper introduces Proportional Reward Splitting (PRS), a reward mechanism that leverages low-work objects called workshares to approximate miners’ power and split rewards proportionally. Theoretical analysis shows PRS achieves fairness and equilibrium properties for sufficiently large parameter values, paralleling FruitChains’ guarantees.

However, FruitChains’ provable guarantees rely on unrealistically large parameters (e.g., long recency/finality windows), and PRS similarly achieves its formal guarantees only for large parameter regimes. The authors explicitly state that establishing comparable game-theoretic security guarantees (fairness and equilibrium) for mechanisms under realistic, small finality windows remains unresolved.

References

Therefore, the question whether a reward mechanism can be proven game theoretically secure for practical parameter values, instead of unrealistically large ones, remains open.

— Optimal Reward Allocation via Proportional Splitting  (2503.10185 - Aumayr et al., 13 Mar 2025) in Section Conclusion

It remains unclear whether their idealized notion of fair sequencing can be realized in practice.

— Otter: A Provably MEV-Resilient Automated Market Maker via Surplus Redistribution  (2609.03474 - Shi et al., 3 Sep 2026) in Section 1, subsection “Additional Related Work,” paragraph “Comparison with closely related work”