We study competition between wireless devices with incomplete information about their opponents. We model such interactions as Bayesian interference games. Each wireless device selects a power profile over the entire available bandwidth to maximize its data rate (measured via Shannon capacity), which requires mitigating the effect of interference caused by other devices. Such competitive models represent situations in which several wireless devices share spectrum without any central authority or coordinated protocol. In contrast to games where devices have complete information about their opponents, we consider scenarios where the devices are unaware of the interference they cause to other devices. Such games, which are modeled as Bayesian games, can exhibit significantly different equilibria. We first consider a simple scenario where the devices select their power profile simultaneously. In such simultaneous move games, we show that the unique Bayes-Nash equilibrium is where both devices spread their power equally across the entire bandwidth. We then extend this model to a two-tiered spectrum sharing case where users act sequentially. Here one of the devices, called the primary user, is the owner of the spectrum and it selects its power profile first. The second device (called the secondary user) then responds by choosing a power profile to maximize its Shannon capacity. In such sequential move games, we show that there exist equilibria in which the primary user obtains a higher data rate by using only a part of the bandwidth.  In a repeated Bayesian interference game, we show the existence of reputation effects: an informed primary user can "bluff" to prevent spectrum usage by a secondary user who suffers from lack of information about the channel gains. The resulting equilibrium can be highly inefficient, suggesting that competitive spectrum sharing is highly suboptimal. This observation points to the need for some regulatory protocol to attain a more efficient spectrum sharing solution.
Adlakha et al. REF proposed a Bayesian game with incomplete interference information about opponents.
Competition in Wireless Systems via Bayesian Interference Games
ArXiv
ArXiv
Computer Science