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Price Differentiating

E$-$commerce websites "alter results depending on whether consumers use smartphones or particular web browsers" ${?}^1,$ reports a new study. The researchers created clean accounts without cookies or browser history and then searched for specific items at different websites using different devices and browsers. On one travel site, for example, prices given for hotels were cheaper when using Safari on an iPhone than when using Chrome on an Android. At Home Depot, the average price of $20$ items when searching from a smartphone was $$230,$ while the average price when searching from a desktop was $$120.$

Let group $1$ be smartphone users and group $2$ be desktop users.

${?}^1$ Ehrenberg R$,"$E$-$commerce sites personalize search results to maximize profits," Science News, November $29,2014.$