Local supplier rescue and relayable liquidity

This article develops a model of sequential supplier rescue in rooted supply trees. An active customer can meet a direct supplier’s fixed activation requirement, but relationship-specific support cannot finance more remote suppliers. Activation instead releases the supplier’s own contingent liquidity, which may be used to rescue its direct suppliers. For any finite tree, the article characterizes equilibrium rescue reach recursively. The homogeneous benchmark yields a sharp reversal in topology rankings: when each node can finance one rescue, a line rescues all suppliers whereas a star rescues only one; when several rescue units are concentrated at the root, the line rescues only its first supplier, while the star rescues as many suppliers as the root can finance. On a fixed line, rescuing q suppliers requires exactly q activation units, and a relay allocation attains this bound. Rescue outcomes therefore depend jointly on network structure and the distribution of liquidity across firms, rather than on either network structure or aggregate liquidity alone.