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The price of free spectrum to heterogeneous users

Adding unlicensed spectrum, such as the recent opening of the television white spaces in the US, has the potential to benefit customers by increasing competition, but may also increase congestion. In an earlier paper, we presented a model for studying the effects of adding unlicensed spectrum to an existing allocation of licensed spectrum among incumbent service providers. Assuming that customers choose providers based the sum of announced price and a congestion cost, it was shown that the social welfare can decrease with additional spectrum. Here we extend this work in two key ways. First, in the earlier work all customers traded-off congestion costs with announced prices in the same way. Here, we consider a heterogeneous pool of customers who may have different trade-offs. Second, the earlier work focused on the overall welfare including both that of service providers and customers. Here we characterize customer surplus as well as total welfare. In particular we show that with homogeneous customers, customer welfare is non-decreasing, while with heterogeneous ones it can decrease.