A dynamic colonel blotto game model for spectrum sharing in wireless networks

Motivated by many real world examples such as communication of mobile devices, localized Internet of Things (IoT) devices, or even autonomous vehicles, and aiming to capture the influence of spectral allocation in a competitive environment on the performance of communication devices, we introduce and study the problem of dynamic competitive spectrum allocation. A scenario of two network service providers (NSPs) who are competing over a period of time to provide wireless connectivity to a set of users is considered. The NSPs compete with one another to gain access to the users by strategically offering the limited available resources to maximize their total payoff. The users accept the best offer made by NSPs which is the bandwidth that maximizes their utility functions. Under such an architecture, this paper focuses on the optimal policy bandwidth allocation strategies for the NSPs over a period of time. Under the condition of dynamically varying spectrum availability at each NSP, we show that the dynamic process of spectrum allocation can be described as a two level game in which the upper level is modeled as an optimal control problem and the lower level is modeled using a classical problem in game theory called the Colonel Blotto game-a multidimensional strategic resource allocation game. We adopt a dynamic non-cooperative repeated game as the decentralized approach for the NSPs to determine their optimal strategies for the next time slot. We also provide the optimal strategy and value function of the dynamic game using Dynamic Programming (DP) and validate it using numerical simulations.