Answer: —
Theorem 2 — class: algorithmic
PDF text-layer excerpt — equations and symbol order may be approximateSuppose all traders have GS valuations. Then the expected competitive ratio of MIDA is at least: 1 −18 · M 2G+2 · c · ln (10Gkmax) √kmax −o(1/kmax) where G is the number of good-kinds, M the maximum number of units of a single good traded by a single per- son, kmax the largest market-size of a single good, and c = kmax/kmin = the largest ratio between market-sizes. Note that previously it was not known if asymptotic opti- mality is possible even with two goods (G = 2). Therefore, it is encouraging that we can get asymptotic optimality for a constant number of goods.
statement extracted from the paper’s text layer; consult the paper for the exact wording
Given a finite support of complete trader types with rational masses \(\mu_t\), explicit gross-substitutes valuations, and integral bundles, compute a price vector \(p\) and type-level allocation masses \(y_{t,a}\) that clear every good, maximize total gain from trade, and use only actions maximizing each type’s gain net of prices; characterize the running time in the number of goods, support size, input bit length, and valuation-table size.
Tier: machine-proved, adversarially reviewed by an independent model. No human has checked this proof. Generated from pipeline artifacts by tools/atlas_build.py.