Search Distortion

Consider a version of Eliaz and Spiegler model. Suppose that v is distributed uniformly on [0, 1], and relevance parameter ? takes two values, 1/2 and 1: Pr(? = 1) = ? and Pr(? = 1/2) = 1 ? ?. Let search cost be equal to s.

1 Search Distortion Consider a version of Eliaz and Spiegler model. Suppose that 'U is distributed uniformly on [0, 1], and relevance parameter 9 takes two values, 1/2 and 1: Pr(6 = 1) = o: and Pr(6 = 1/2) = 1 a. Let search cost be equal to s. 1. Suppose that the search engine induces expected relevance 03. Show that consumer reservation values 18 2 'v*=1 8 BE 2. What is the price charged by a rm of quality 19 and its prot? 3. Express search engine's fee and prot in terms of 9*, 63 and s. 3% 4. Suppose that a = 1/8. What is search engine's prot if it induces high relevance, i.e. 0* = 1'? What if its prot when it induces distorts search, i.e. 6* = 1/2? Which fee should search engine choose? Firm pricing 0 In firms' pricing problem, first thing to notice is that the per-click fee does not affect the pricing decision directly 0 A firm has to pay r once a consumer clicks in, no matter whether the transaction is successful or not, and, thus, r is taken as sunk 0 A firm with quality 6 solves the following problem mFax p9(1 F(v* p* + p)), which yields an: _ 1 F(V*) p _ aw) Consumer search ' Only firms with the relatively high relevance will enter the search pool. Define the cut-off type as 6* and only firms with 9 2 6* enter the search pool; denote 69:E(6|629*) ' Consumers' optimal stopping rule is determined by the reservation price v* as (z v*)dF(z) : 5 De rivation A consumer, who expects equilibrium price p*, stops and buys if v p 2 v* p* and continues on searching if otherwise ' The term in the front is the conditional expectation of relevance. Consumers take into account that a match is of positive value only with average probability Be .. q _ _ a\\. _ _ w.. Search engine 0 A monopoly search engines controls the quality of the search pool ' It chooses quality level 6"\" so only firms with 19,- 2 9* appear in the search pool 0 The search engine does not need to directly control 9*. but can implement any 6* by setting per-click fee r ' this is a payment from firms to the search engine each time a consumer visits the firm. which is independent of whether the transaction is successful or not ' only firms that accept the per-click fee are allowed to enter the search pool ' Only firms with high enough quality will enter the pool since their expected profits are high enough to compensate the payment to the search engine Firms The model is based on Eliaz and Spiegler (EJ, 2011) A large (infinite) number of firms producing differentiated products Firms reach their customers via a monopolistic search engine Firms are vertically differentiated w.r.t. the quality (relevance): 6 6 [0,1] which is distributed according to 6(9) If firm f's relevance is 6;. a consumer obtains match value 0 with probability 1 6;, and match value v with probability 6;, where v is randomly drawn from a common distribution F on [0,1] a horizontal part of product differentiation roduction Search Pool C Auctions Mechanism Design Appendix Firm quality and search duration . Next consider search duration ge(1 - F(v*) ) . Increasing 0* has an ambiguous effect on search duration . 0* increases = @ increases . 0* increases = 1 - F(v*) decreasesFirm quality and per-click fee ' 19" increases in 9* 0 First. consider the equilibrium perclick fee X (1 Fm r* : conv. rate x p* : 6*(1 F(v*)) f0\") 0 Increasing 6* has an ambiguous effect on equilibrium perclick fee 0 6* increases 2: v* increases :> p'\" decreases 0 6* increases 2; conversion rate can go either way Search engine (cont.) . The search engine maximizes its expected profit, which equals the per-click price times the expected number of clicks (expected search duration) r max E(0e(1 - F(v*) ) . Plug in the expression of r from previous slide, the maximization problem becomes max 0* 1 - F(v*) f (v*)Equilibrium profit and search duration 0 A type6 firm's em profit is 9(1 F(v'\"))2 f(v*) 0 Equilibrium expected conversion rate is 69(1 F(v*)) \"(9) : P*9(1 Flt/\"7) : 0 Equilibrium expected search duration is the inverse of the expected equilibrium conversion rate, 1/[HE(1 F(v*))]