Non-cooperative computation: Boolean functions with correctness and exclusivity

We introduce the concept of non-cooperative computation (NCC), which is the joint computation of a function by self-motivated agents, where each of the agents possesses one of the inputs to the function. In NCC the agents communicate their input (truthfully or not) to a trusted center, which performs a commonly-known computation and distributes the results to the agents. The question is whether the agents can be incented to communicate their true input to the center, allowing all agents to compute the function correctly. NCC is a game theoretic concept, and specifically is couched in terms of mechanism design. NCC is a very broad framework, and is specialized by imposing specific structure on the agents’ utility functions. The technical results we present are specific to the setting in which each agent has a primary interest in computing the function, and a secondary interest in preventing the others from computing it (properties called correctness and exclusivity). For this setting we provide a complete characterization of the Boolean functions that are noncooperatively computable. We do this for three versions of NCC: a basic deterministic version, a probabilistic version, and a version in which the computation can be subsidized by the center. The analysis turns out to depend on whether the inputs of the agents are probabilistically correlated or not, and we analyze both cases. 1This work was supported by NSF grant IIS-0205633.