Immobility, Rationing and Price Competition

A model is studied where firms advertise prices and buyers play a noncooperative search game in an attempt to secure output from firms at the advertised prices. Firms face rising marginal costs and may not be willing to supply everything demanded at their price if they wind up with many buyers. It is shown that rationing will occur in equilibrium no matter how averse buyers are to this possibility. The result is specialised to a case where rationing occurs with probability one. The equilibrium price and outputs are characterised for this case.