Multi-product Dynamic Pricing Policy Under Reference Effects

There are some products that consumers repeatedly purchase.Based on the memory of past prices and the comparison with competitive goods,consumers generate a price expectation,which is called reference price.Consumers always compare the reference point with the current actual price and generate a sense of "acquisition" or"loss" from the discrepancy,which is likely to influence the purchase decision.In consideration of the research status and realistic situation,this paper pays attention to the multi-product dynamic pricing under the reference effects.Specifically,most of the existing research is a single product issue and has not been extended to a multi-product scenario.In addition,compared to selling only one kind of goods,it is more common for merchants to sell multiple products.For example,beverage stores sell a variety of beverages,and sports flagship stores sell a variety of seasonal sports pants.We assume that the reference price in the multi-product issue is not only related to its own historical price but also the prices of other commodities.We get into the three cases of the lowest price,the highest price and the average price of the multi-products as the previous price level,and then adopt the exponential smooth mechanism to update reference price.In this setting,we conclude the optimal pricing strategies for multiple products managed by a monopolist,including the existence of steady state,steady-state price levels and the changes.Through numerical experiments,we explore the following factors that influence the optimal pricing policy,that is the relationship of multi-products,the price level mechanism adopted by consumers,the emotional intensity of consumers,the memory and the loss attitude.We summarize the management implications of how to jointly price multi-products to maximize long-run revenue.It sums up the general rules and special circumstances.Generally,when the consumers are loss neutral or loss aversion,the price path converges to a steady state.However,the steady price of each product may not be the same,depending on system parameters.The determination needs to combine the discrepancy among products(the difference of market capacity and price sensitivity),the price mechanism adopted by consumers,the memory of consumers and the intensity of emotions to examine.When consumers are loss seeking,the optimal pricing strategy is usually a shock strategy,that is,high-low price alternating.The conclusions of this paper have important practical guiding significance for merchants selling multi-products,especially when consumers are loss neutral or loss aversion.In the long-term perspective,pricing will eventually be fixed.In addition,merchants need to fully examine product characteristics,product relationships,consumer types and characteristics to determine whether each product is at the same fixed price level.