Blindly-competitive Algorithms: Pricing & Bidding as a Case Study

The standard setting for competitive analysis of online algorithms assumes that on-line algorithm knows the past (but not future) inputs, and can optimize its performance by \learning" from mistakes of the past. This framework cannot capture some of the real-life online decision-making, which takes place without full knowledge of past and present inputs. Instead, online algorithm only knows a function (or part) of its past decisions and real inputs (which we call the hidden input). A typical example is that of economic \warfare" involving, say, two companies, and a pool of (unknown) customers. In this work, we focus on problem of pricing an interdependent collection of resources , in the absence of knowledge about the following crucial information about the past and future inputs: the customers nancial beneet or prices ooered by the competition, the duration of the contracts, and the future demand for the products. Can we achieve \competitive" proot, i.e., proot comparable to that of an \insider trader", who knows exactly the hidden input (e.g. what the competition is doing) , as well as the future demand ? This paper answers this question in the aarmative, by presenting an \optimally-blindly-competitive" pricing strategy, whose competitive factor grows only logarithmically in price range. As a case study, we apply our methods to the problem of competitive online pricing of telephone networks.