Price-Matching in a Sequential Search Duopoly. Aleksandr Yankelevich Department of Economics Washington University in St. Louis

Transcription

1 Price-Matching in a Sequential Search Duopoly Aleksandr Yankelevich Department of Economics Washington University in St. Louis

2 Competitor Based Price Clauses Competitor Based Price Clauses: any price guarantee where the firm s price is a function of the price of a rival firm (e.g., low-price guarantee) Price-Matching Guarantee: a guarantee to set the firm s price to that of a rival upon consumer request 63% of low-price guarantees are price-matching guarantees (Arbatskaya, Hviid and Shaffer 2004) Page 2 of 33

3 Examples : Offers price-matching guarantee. Our goal is always to be the low price leader in every community where we operate. Our customers trust us to have everyday low prices... there's no need for special sales. kmart: No price-matching guarantee offered. : Offers price-matching guarantee. If you find a lower advertised price for the same item, we ll match it! Simply bring in the printed ad from a local competitor for almost any item we have in-stock!... Not applicable to Internet prices or ads. : No price-matching guarantee offered. Page 3 of 33

4 The Price-Matching Debate Question: Is the practice of price-matching anti-competitive or procompetitive? Anti-competitive Effects: Tacit Collusion: Hay 1982, Salop 1986, Belton 1987, Doyle 1988, Zhang 1995, Hviid and Shaffer 1999 Price Discrimination: Png and Hirshleifer 1987; Edlin 1997; Corts 1996; Chen, Narasimhan, and Zhang 2001 Page 4 of 33

5 The Price-Matching Debate Question: Is the practice of price-matching anti-competitive or procompetitive? Pro-competitive Effects: Low Cost Signaling: Moorthy and Winter 2006, Moorthy and Zhang 2006 Opportunistic Search: Chen, Narasimhan, and Zhang 2001; Janssen and Parakhonyak 2009 Page 5 of 33

6 Why Sequential Search? Allows us to ask the question: How do price-matching guarantees affect consumer incentives to invest in information about prices? Using a sequential search framework to endogenize consumers decisions to shop for prices, we can show how price-matching affects: i. where consumers begin their price search. ii. consumers decision to search the second firm. iii. consumers final purchasing decision. Page 6 of 33

7 Findings Price-matching raises prices in three distinct ways. 1. Tacit collusion: i. Price-matching hampers firms ability to capture consumers by running bigger sales ii. Because consumers engage in optimal sequential price search, monopoly pricing almost never occurs Page 7 of 33

8 Findings 2. Search activity declines: i. Some consumers require higher price observations to induce them to search beyond the first firm ii. Not all consumers choose to obtain all available price information. This allows firms to price discriminate. Page 8 of 33

9 Findings 3. Asymmetric equilibria: i. Even though firms are ex-ante symmetric, in equilibrium, the proportion of consumers that begin their search in each firm may be different ii. There is a multiplicity of such equilibria iii. The more asymmetric the equilibrium, the lower consumer welfare Page 9 of 33

10 Model (Firms) Price-Matching in a Sequential Search Duopoly Two firms sell a homogenous good. Firms have no capacity constraints and have identical constant cost of 0 of producing one unit of the good. Both firms can choose to offer price-matching guarantees. guarantees are legally enforceable. The Page 10 of 33

11 Model (Consumers) Price-Matching in a Sequential Search Duopoly Unit mass of almost identical consumers with unit demand for the good and valuation v 0. Consumers a priori uninformed about prices. 0, 1 of the consumers have 0 search cost (shoppers). Remaining 1 consumers (non-shoppers) must pay search cost c 0, v to visit the second firm. Recall is costless all consumers can freely choose the cheapest price they ve observed. Page 11 of 33

12 Model (Consumers) Price-Matching in a Sequential Search Duopoly 0, 1 S shoppers ignore price-matching guarantees and always purchase from the firm with the lower listed price. 1 S shoppers invoke price-matching guarantees at the last firm they stopped in when one is available and necessary to obtain the lower price there. Otherwise, they purchase from the firm with the lower listed price. Page 12 of 33

13 Game (Firms) Price-Matching in a Sequential Search Duopoly Stage 1: Firms simultaneously decide whether or not to offer a legally binding price-matching guarantee. The outcome of each firm s decision becomes common knowledge before the next stage. Stage 2: Firms simultaneously choose prices. Page 13 of 33

14 Game (Consumers) Price-Matching in a Sequential Search Duopoly Stage 3: Consumers choose an optimal search strategy given their beliefs about firm pricing strategies. All consumers search sequentially. Consumers decide which firm to enter first. Consumers choose whether or not to search the second firm after freely obtaining the first price sample. Consumers decide whether or not to buy the product. Consumers decide where to buy the product. Page 14 of 33

15 Non-Shopper Search Behavior After freely observing a price at firm i, a non-shopper searches firm j only if the observed price at firm i is no less than his reservation price, given equilibrium price distribution F. Reservation Price r i is the solution to: j r i ( r i p)d Fi( p) c (1) p Marginal Cost Marginal Benefit of Search of Search Page 15 of 33

16 Equilibrium Concept Price-Matching in a Sequential Search Duopoly Sequential Equilibrium i. Consumers and firms behave optimally at every decision node given other players strategies. ii. Consumers treat out of equilibrium prices at the first firm sampled as mistakes when forming beliefs about the remaining firm s strategy that is, consumers believe that unsampled firms play their equilibrium strategies at all information sets. Page 16 of 33

17 Equilibrium (Baseline Model No Price-Matching) Stahl (1989) There is a symmetric equilibrium in mixed pricing strategies. i. Mass points are always undercut to capture shoppers. ii. Marginal cost pricing does not occur because a firm can always raise prices to profit from non-shoppers. In equilibrium, the reservation price, r, is never below the upper bound of the firm price distributions. Non-shoppers never search. Page 17 of 33

18 Equilibrium (Baseline Model No Price-Matching) F 1 F p Unique Symmetric Equilibrium: F F F, p1 p2 p, 1 2 p1 p2 p min r, v p p p Mixed pricing strategies can be interpreted as price dispersion that is, firms run sales of varying size. The distribution function is concave. Big sales are more common. Page 18 of 33

19 Equilibria with Price-Matching There are two types of equilibria: i. Both firms offer price-matching guarantees on the equilibrium path ii. Only one firm offers a price-matching guarantee on the equilibrium path There is a multiplicity of both types of equilibria, which vary in the proportion of consumers who start searching at a particular firm Page 19 of 33

20 Symmetric Equilibrium (Both Firms Price-Match on Equilibrium Path) Price distribution first-order stochastically dominates baseline price distribution. i. Not all shoppers purchase from the firm with the lower price. ii. Non-shoppers anticipate higher prices and are willing to accept higher prices at the first firm sampled. 1 2 Let S S. The price distribution with dominates the price distribution with. 2 S 1 S first-order stochastically Page 20 of 33

21 Symmetric Equilibrium (Both Firms Price-Match on Equilibrium Path) F p S v 4.15 c p Page 21 of 33

22 Symmetric Equilibrium (Both Firms Price-Match on Equilibrium Path) Proposition. Suppose S 0 and that both firms offer price-matching guarantees on the equilibrium path. Then there exists a unique Sequential Equilibrium where both firms chose price v, and the reservation price is greater than v., p min r 1, r2, v shoppers, but all prices below min r1, r2, v If 0 S proportion of non-shoppers.. Lower prices never attract additional attract the same From Equation (1) we know that min 1, 2 r r v. So, p p v! Page 22 of 33

23 Asymmetric Equilibria (Both Firms Price-Match on Equilibrium Path) Define S 0, 1 0, 1 as the equilibrium fraction of shoppers and N as the equilibrium fraction of non-shoppers who begin their search at firm 1. In equilibrium, firm i is indifferent between any price in its support. For firm 1, this gives: p F p p E, E (2) i i j i i E p F p p p p F p 1 S S S 2 1 S S p p 1 1 N 1 SS S N Page 23 of 33

24 Asymmetric Equilibria (Both Firms Price-Match on Equilibrium Path) We can use Equation (2) to solve for F 1 and F 2 as functions of, S, p, and the s. Then use Fi p 1 to solve for p in terms of p and use Equation (1) to solve for the reservation price. In equilibrium, consumers are indifferent between which firm to search first. Thus, for a given value of N, we can use indifference condition E1 p E2 p to solve for a unique value of S as a function of, S, and c. Page 24 of 33

25 Asymmetric Equilibria (Both Firms Price-Match on Equilibrium Path) F, F i j 1 Fj p Fi p Multiple Asymmetric: E p E p 1 2 p min r, r, v 1 2 p p p Both firms have concave distribution functions, but firm j tends to run sales less frequently. Expected prices in both firms are equal. Intuition: Price-matching allows some shoppers to obtain the lowest price in either firm. Suppose a larger proportion of non-shoppers begins their search at a particular firm. As long as a larger proportion of shoppers is expected to buy from the other firm, expected prices in both firms can be equal and all consumers are indifferent with regard to the search order. Page 25 of 33

26 Asymmetric Equilibria (Both Firms Price-Match on Equilibrium Path) For a given value of S, consumers are better off in the symmetric equilibrium. i. The firm that expects to serve more non-shoppers loses more profit than in a symmetric equilibrium when lowering prices. ii. The firm that expects to serve more shoppers no longer needs to lower prices as much to retain the same proportion of shoppers. As the amount of asymmetry that prevails in equilibrium increases, consumer welfare declines. Page 26 of 33

27 Equilibrium (Only One Firm Matches on Equilibrium Path) No symmetric equilibrium. The shape of the distribution functions is the same as in previous min r, r, v again serving as the upper asymmetric equilibria, with 1 2 bound of both firm supports. The non-matching firm is the one with the atom at p! The non-matching firm runs fewer sales than it would if neither firm offered price-matching guarantees to exploit a larger number of nonshoppers that search it first. Knowing that it will have fewer non-shoppers, the other firm offers price-matching guarantees to increase the expected number of shoppers that it captures in equilibrium. Page 27 of 33

28 Summary Equilibrium: In equilibrium, either both firms will offer price-matching guarantees or only one firm will offer a price-matching guarantee. In any equilibrium outcome where firms are given the option of offering pricematching guarantees, expected prices and firm profits are higher than when price-matching is not an option. Comparative Statics: Given firms equilibrium price-matching decisions, expected prices and firm profits are increasing in the proportion of shoppers using price-matching guarantees and in the amount of asymmetry (difference in number of non-shoppers between the two firms). Page 28 of 33

29 Conclusion Price-matching guarantees improve firm profits at consumer expense: i. They decrease firms incentives to lower prices. ii. They raise non-shopper reservation prices. iii. They can lead to asymmetric equilibria with fewer sales and higher prices than in the symmetric case. Page 29 of 33

30 Extensions Survey test of model: Ask individuals who use price-matching guarantees to secure the lowest price if they would obtain that price regardless by purchasing elsewhere. If the answer is yes, the model setup is sound. Use firms that are ex-ante asymmetric with respect to the cost of producing the good. i. Asymmetric equilibria in an ex-ante asymmetric framework may lead to pro-competitive effects of price-matching. ii. Current formulation tells us that cross-sectional empirical tests need to take firm production costs into account. Page 30 of 33

31 Price- Matching Page 31 of 33

32 Previous Literature (Empirical Findings) Firms with LPGs have lower prices (Moorthy and Winter 2006, Moorthy and Zhang 2006, Arbatskaya, Hviid and Shaffer 2006). Firms with LPGs force competitors to lower prices (Mañez 2006). Firms with LPGs have higher prices (Hess and Gerstner 1991, Arbatskaya, Hviid and Shaffer 2006). Most LPGs are associated with high hassle costs, and price-beating guarantees more so than price-matching guarantees (Arbatskaya, Hviid and Shaffer 2004). Page 32 of 33

33 Previous Literature (Experimental Findings) Consumers perceive price-matching firms to have lower prices (Jain and Srivastava 2000, Jain and Lurie 2001). Price-matching always raises prices, but cost asymmetries and hassle costs can offset price increases (Dugar and Sorensen 2006, Fatas and Mañez 2007, Mago and Pate 2009). Page 33 of 33