  Task allocation is a crucial process in modern systems, but it is often
challenged by incomplete information about the utilities of participating
agents. In this paper, we propose a new profit maximization mechanism for the
task allocation problem, where the task publisher seeks an optimal incentive
function to maximize its own profit and simultaneously ensure the truthful
announcing of the agent's private information (type) and its participation in
the task, while an autonomous agent aims at maximizing its own utility function
by deciding on its participation level and announced type. Our mechanism stands
out from the classical contract theory-based truthful mechanisms as it empowers
agents to make their own decisions about their level of involvement, making it
more practical for many real-world task allocation scenarios. It has been
proven that by considering a linear form of incentive function consisting of
two decision functions for the task publisher the mechanism's goals are met.
The proposed truthful mechanism is initially modeled as a non-convex functional
optimization with the double continuum of constraints, nevertheless, we
demonstrate that by deriving an equivalent form of the incentive constraints,
it can be reformulated as a tractable convex optimal control problem. Further,
we propose a numerical algorithm to obtain the solution.
