The impact of investment timing and uncertainty on competition in unlicensed spectrum

There has been much interest in expanding the amount of unlicensed spectrum available for wireless services. Such spectrum reduces the barriers to entry by removing the need to purchase expensive licenses and so may lead to increased competition. However, this spectrum also has the risk of becoming over-congested, which could deter service providers from investing and offering service. Recent work has studied this trade-off by considering game theoretic models where service providers first make decisions to invest and then subsequently compete for customers. In such cases, the only Nash equilibria are often for a single service provider to enter and act as a monopolist. These conclusions are based on a model where service providers simultaneously make investment decisions with full knowledge about their competitors' costs. Here, we relax these assumptions and consider more realistic scenarios where service providers make investment decisions at different times and also consider cases where these decisions are made with incomplete information about the other service provider's costs. For a class of such games, we characterize the resulting Nash equilibria and show that differences in timing and uncertainty lead to a richer class of possible equilibria.