Uniqueness of equilibrium in a payment system with liquidation costs

We study a financial network where forced liquidations of an illiquid asset have a negative impact on its price, thus reinforcing network contagion. We give conditions for uniqueness of the clearing asset price and liability payments. Our main result holds under mild and natural assumptions on the price impact function: monotonicity of the price impact function and strict monotonicity of the proceeds of liquidation in the liquidated quantity.