Monotone equilibrium in matching markets with signaling

We introduce a notion of competitive signaling equilibrium (CSE) in one-to-one matching markets with a continuum of heterogeneous senders and receivers. We then study monotone CSE where equilibrium outcomes - sender actions, receiver reactions, beliefs, and matching - are all monotone in the stronger set order. We show that if the sender utility is monotone-supermodular and the receiver's utility is weakly monotone-supermodular, a CSE is …