Near‑optimality of modified EIP‑1559 under a global discount rate

Prove that the modified EIP‑1559 algorithm that evaluates eligibility using the current discounted value v_i(1−ρ)^{t−t_i} for each transaction i is near‑optimal in social welfare when all transactions share the same global discount rate ρ, under the same average block size framework used in the paper.

Background

For partially patient bidders (time‑discounted values), the paper shows that no online algorithm can achieve near‑optimal welfare when discount rates vary across transactions. A natural modification is to let EIP‑1559 compare transactions by their current discounted values.

The authors conjecture that when the discount rate is global (shared by all transactions), this modified EIP‑1559 should still be near‑optimal, potentially with an additional loss depending on ρ. Establishing such a result would delineate precisely when partial patience can be accommodated efficiently.