  In a multi-party machine learning system, different parties cooperate on
optimizing towards better models by sharing data in a privacy-preserving way. A
major challenge in learning is the incentive issue. For example, if there is
competition among the parties, one may strategically hide his data to prevent
other parties from getting better models.
  In this paper, we study the problem through the lens of mechanism design and
incorporate the features of multi-party learning in our setting. First, each
agent's valuation has externalities that depend on others' types and actions.
Second, each agent can only misreport a type lower than his true type, but not
the other way round. We call this setting interdependent value with
type-dependent action spaces. We provide the optimal truthful mechanism in the
quasi-monotone utility setting. We also provide necessary and sufficient
conditions for truthful mechanisms in the most general case. Finally, we show
the existence of such mechanisms is highly affected by the market growth rate
and provide empirical analysis.
