Competitive pricing with dynamic asymmetric price effects

We model the temporal pricing strategies for two firms with asymmetric costs and differing market power (i.e. big-box retailer versus smaller local merchant). A firm's demand is a function of its price, a reference price and its competitor's price. Price effects may be asymmetric, i.e. consumers respond differently if they perceive a good to be over-priced versus under-priced. We derive analytical results for optimal prices. We show through a series of numerical examples under what settings firms choose various pricing strategies as well as profit implications for firms with differing costs.