Robust Welfare Decentralization under Population Entry

Abstract

We ask when an incumbent economy with indivisible goods can accommodate an arbitrary new participant while retaining an efficient allocation supported by anonymous item prices. We call this property universal entry robustness. An economy is universally entry-robust if and only if its aggregate welfare valuation is additive. Although the requirement quantifies over all entrant valuations, it can be tested using one canonical entrant whose value for a bundle equals the loss in maximal incumbent welfare caused by removing that bundle. When the characterization holds, one uniquely determined price vector decentralizes the incumbent optimum and every one-agent extension. The proof is direct and uses only demand optimality and welfare comparisons, making transparent why arbitrary-entry robustness eliminates all bundle interactions in aggregate welfare. We finally relate this argument to the robust-integrality interpretation obtained from the linear-programming characterization of Bikhchandani and Mamer (1997). Individual incumbent valuations may be nonadditive and need not satisfy gross substitutes.