Many-to-many matching on a skill-sharing platform

Each agent in a market needs to supplement his skill with a particular skill of another agent to complete his project. A platform matches the agents and allows members of the same match to share their skills. A match is valuable to an agent if he is matched with any agent who possesses a skill complementary to his own skill. When the platform uses the divide-and-conquer pricing strategy, we study the properties of incentive compatible mechanisms in relation to the reciprocal property of the complementary relationships among different skills, and when the market expands in its size.