We prove existence of a stationary residual-rivalry MPE, es…

We prove existence of a stationary residual-rivalry MPE, establish uniqueness on smooth economic regions using a variational-inequality monotonicity argument, and show that hard residual-exit boundaries create a separate boundary layer in which the equilibrium correspondence can branch.
That branching is economically meaningful: near exit, residual predation becomes a coordination problem over which firm pays the cost to push the rival across the liquidity boundary.