We consider price competition models for oligopolistic markets, in which the consumer reacts to relative rather than absolute prices, where the relative price is defined as the difference between the absolute price and a given reference value. Such settings arise, for example, when the full retail price earned by the 'retailer' is reduced by virtue of a third party offering a subsidy or a rebate or in prospect theoretical models in which customers establish a reference price and base their choices on the differentials with respect to the reference price. When choosing among the various competing options, the consumer trades off the net price paid with various other product or service attributes, as in standard price competition models. The reference price may be exogenously specified and pre-announced to the competing firms. Alternatively, it may be endogenously determined, as a function of the set of absolute prices selected by the competing firms, for example the lowest or the second lowest price. We review five different application areas where the above model structure arises. We then characterize the equilibrium behavior under a general reference value scheme of the above type; this in a base model, where we assume that the consumer choice model is of the general MultiNomialLogit (MNL) type. We also derive comparison results for the price equilibria that arise under alternative subsidy schemes. These comparisons have important implications for the design of subsidy schemes
