Multidimensional signaling in the labor market

I consider a two-dimensional job market signaling model in which firms care about a worker's personal network as well as his technical productivity, and a worker can choose both academic activity and social activity to signal his ability. In a simple model where the social activity forming a social network does not require special ability, I show that the Cho-Kreps intuitive criterion singles out Spence's outcome of signaling high academic ability by high education. I also demonstrate the possibility that a worker with high academic ability may underinvest in education when the social ability is correlated with the academic ability.