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This is an economic research paper on the role of pricing algorithms in online markets. It does not include any legal analysis. It reviews some existing literature, arguments, and evidence on the effects of pricing algorithms on competition. It discusses collusion and personalised pricing, as well as potential benefits to consumers, and considers what characteristics of markets or pricing algorithms might make collusive outcomes more likely. We carried out a small amount of evidence gathering to fill some literature gaps, including some tests of personalised pricing.