Efficiency and Equilibrium in Task Allocation Economies with Hierarchical Dependencies

We analyze economic e ciency and equilibrium properties in decentralized task allocation problems involving hierarchical dependencies and resource contention. We bound the ine ciency of a type of approximate equilibrium in proportion to the number of agents and the bidding parameters in a particular market protocol. This protocol converges to an approximate equilibrium with respect to all agents, except those which may acquire unneeded inputs. We introduce a decommitment phase to allow such agents to decommit from their input contracts. Experiments indicate that the augmented market protocol produces highly efcient allocations on average.