  Multi-agent coordination problems often require agents to exchange state
information in order to reach some collective goal, such as agreement on a
final state value. In some cases, it is feasible that opportunistic agents may
deceptively report false state values for their own benefit, e.g., to claim a
larger portion of shared resources. Motivated by such cases, this paper
presents a multi-agent coordination framework which disincentivizes
opportunistic misreporting of state information. This paper focuses on
multi-agent coordination problems that can be stated as nonlinear programs,
with non-separable constraints coupling the agents. In this setting, an
opportunistic agent may be tempted to skew the problem's constraints in its
favor to reduce its local cost, and this is exactly the behavior we seek to
disincentivize. The framework presented uses a primal-dual approach wherein the
agents compute primal updates and a centralized cloud computer computes dual
updates. All computations performed by the cloud are carried out in a way that
enforces joint differential privacy, which adds noise in order to dilute any
agent's influence upon the value of its cost function in the problem. We show
that this dilution deters agents from intentionally misreporting their states
to the cloud, and present bounds on the possible cost reduction an agent can
attain through misreporting its state. This work extends our earlier work on
incorporating ordinary differential privacy into multi-agent optimization, and
we show that this work can be modified to provide a disincentivize for
misreporting states to the cloud. Numerical results are presented to
demonstrate convergence of the optimization algorithm under joint differential
privacy.
