Price Promotions: Limiting Competitive Encroachment

In this paper we explore equilibrium pricing strategies in an infinite horizon repeated game for an oligopoly. In a model where two symmetric firms (out of three) have a loyal customer base, it is shown that if there are sufficiently large number of switchers in the market and the firms are have a sufficiently how discount rate (high discount factor), the resulting equilibrium strategies take the form of alternating promotions between the two leading firms. Extending the model to allow for variations in the number of swtichers from period to period, number of loyal consumers for the two leading firms and the reservation prices for their two premium brands leads us to hypothesize the relationship between these factors and the depth and frequency of discounts offered by the three firms. Finally, and more generally, we show that price promotions can be interpreted as a long run strategy pursued by leading firms to defend their market share from possible enroachments of the third firm such that the cost of defending their market is shared between the two leading firms