Non-Cooperative Game for Capacity Offload

With the dramatic increase of wireless data traffic, incumbent wireless service providers (WSPs) face critical challenges in provisioning spectrum resource. Given the permission of unlicensed access to TV white spaces, WSPs can alleviate their burden by exploiting the concept of "capacity offload" to transfer part of their traffic load to unlicensed spectrum. For such use cases, a central problem is for WSPs to coexist with others, since all of them may access the unlicensed spectrum without coordination thus interfering with each other. Game theory provides tools for predicting the behavior of WSPs, and we formulate the coexistence problem under the framework of non-cooperative games as a capacity offload game (COG). We show that a COG always possesses at least one pure-strategy Nash equilibrium (NE), and does not have any non-degenerate mixed-strategy NE. The analysis provides a detailed characterization of the structure of the NEs in two-player COGs. When the game is played repeatedly and each WSP individually updates its strategy based on its best-response function, the resulting process forms a best-response dynamic. We establish that, for two-player COGs, alternating-move best-response dynamics always converge to an NE, while simultaneous-move best-response dynamics do not always converge to an NE when multiple NEs exist. When there are more than two players in a COG, if the network configuration satisfies certain conditions so that the resulting best-response dynamics become linear, both simultaneous-move and alternating-move best-response dynamics are guaranteed to converge to the unique NE.