Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for efficiently allocating resources among participants. Methods can include receiving valuation data specifying, for each of a plurality of entities, a respective valuation for each of a plurality of resource subsets, each resource subset comprising a different combination of one or more resources of a plurality of resources. After receiving valuation data, assigning each resource in the plurality of resources to a respective entity of the plurality of entities based on the valuations and generating, for each particular entity, a respective input representation that is derived from valuations of every other entity in the plurality of entities other than the particular entity. The input representation for each particular entity is processed using a neural network to generate a rule for the particular entity and a payment based on the rule output for the entities.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for efficiently allocating resources among participants. Methods can include receiving valuation data specifying, for each of a plurality of entities, a respective valuation for each of a plurality of resource subsets, each resource subset comprising a different combination of one or more resources of a plurality of resources. After receiving valuation data, assigning each resource in the plurality of resources to a respective entity of the plurality of entities based on the valuations and generating, for each particular entity, a respective input representation that is derived from valuations of every other entity in the plurality of entities other than the particular entity. The input representation for each particular entity is processed using a neural network to generate a rule for the particular entity and a payment based on the rule output for the entities.