We consider a model where market participants can observe the identity of the agents they can be matched with but not their types. A mechanism generates a matching and an announcement at each reported type profile. For the case of one-sided incomplete information, we fully characterize the set of matching states which are both minimally informative and stable, and show that not every assortative matching mechanism is ex-post incentive compatible. Our main result states that every seemingly informative assortative matching mechanism is ex-post incentive compatible. Such mechanisms become manipulable when incompleteness of information applies to both sides of the market.
We consider an incomplete information network game in which agents are only aware of the identity of their immediate neighbors. They form beliefs about the links of their neighbors (the rest of the network) and play a linear-quadratic effort game to maximize interim payoffs. We establish the existence and uniqueness of Bayesian-Nash equilibria in pure strategies. In equilibrium, agents use local knowledge of their direct connections to make inferences about the complementarity strength of their actions with other agents given by their updated beliefs regarding their walks in the network. Using this and an example we show that under incomplete information, besides network architecture, agent identity plays a crucial role in determining strategic behavior. We also characterize equilibrium behavior under different forms of ex-ante prior beliefs like uniform priors, Erdos-Renyi network generation, and homophilic linkage. Not surprisingly, uniform priors provide similar results similar to degree-based models of incomplete information.