14.27 — Economics and E-Commerce Lecture 10 - Search and Obfuscation on the Internet Before the exam, we talked about price search and saw one model, Diamond, that said all ﬁrms price at P m in the presence of any search costs at all • knife-edge aspect of pricing seems unrealistic • there is a lot of price dispersion in real life • casual empiricism suggests that degree of price dispersion might be a function of level of search costs First, we must introduce a notion of a mixed strategy. What we’ve encountered so far in games we’ve seen are what are called “pure strategies.” A pure strat egy is a well-deﬁned, non-stochastic action or set of actions. A “mixed strategy” is simple one of a number of pure strategies chosen stochastically with a ﬁxed frequency. • e.g., ﬂip a coin – H → set P = P m – T → set P = c • e.g., game played between pitcher and batter in baseball – strategies: ∗ pitcher: what pitch to throw ∗ batter: whether to prepare for a particular pitch & which one – batter has huge advantage if he knows a fastball or curveball or slider is coming – even though there are some game situations where fastball sort of makes more sense than other pitches, pitcher will still want to employ a mixed strategy of what pitch to throw – batters will also want to employ a mixed strategy between swinging aggressively for a particular pitch or more tentatively to be able to adjust Model ⎧ N ﬁrms produce homogeneous goods ⎪ ⎪ ⎪ ⎪ ⎨ constant, common mc, c continuum of consumers, each with D(P ) same as Diamond ⎪ ⎪ assume (P − c)D(P ) concave ⎪ ⎪ ⎩ ﬁrms simultaneously choose prices P1 , ..., PN • fraction of consumers µ have search cost s ≤ 0 “shoppers” • fraction 1 − µ have search cost s ∼ [s, s̄] with 0 < s < s̄ < cs(P m ) • consumers search optimally and purchase as before 1 Lecture 10 Search and Obfuscation on the Internet Proposition (Stahl, 1989) • the model has no pure strategy NE • there exists a symmetric mixed strategy NE where ﬁrms choose prices from a continuous distribution F with support not containing c –price dispersion. • as proposition of shoppers (µ) goes from 0 to 1, the NE changes continuously from Diamond NE to Bertrand NE • as s and s̄ decrease, the NE converges to Bertrand Notes • Diamond produces extreme result (P m ) with inﬁnitesimal search costs • search costs confer de factor monopoly status on every seller • Diamond also predicts that everyone prices the same –no dispersion • empirical evidence suggests that markets where search costs are substantial exhibit a lot of price dispersion • including a fraction of people who like to shop in the model changes results substantially – price dispersion – doesn’t have knife-edge characteristic like Diamond • in Stahl model, prices increase with increased search costs, which suggests collective incentive of ﬁrms to raise search costs (perhaps not individual) 2

Search and Obfuscation on the Internet

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