We study competition between wireless devices with incomplete informationabout their opponents. We model such interactions as Bayesian interferencegames. Each wireless device selects a power profile over the entire availablebandwidth to maximize its data rate. Such competitive models representsituations in which several wireless devices share spectrum without any centralauthority or coordinated protocol. In contrast to games where devices have complete information about theiropponents, we consider scenarios where the devices are unaware of theinterference they cause to other devices. Such games, which are modeled asBayesian games, can exhibit significantly different equilibria. We firstconsider a simple scenario of simultaneous move games, where we show that theunique Bayes-Nash equilibrium is where both devices spread their power equallyacross the entire bandwidth. We then extend this model to a two-tiered spectrumsharing case where users act sequentially. Here one of the devices, called theprimary user, is the owner of the spectrum and it selects its power profilefirst. The second device (called the secondary user) then responds by choosinga power profile to maximize its Shannon capacity. In such sequential movegames, we show that there exist equilibria in which the primary user obtains ahigher data rate by using only a part of the bandwidth. In a repeated Bayesian interference game, we show the existence of reputationeffects: an informed primary user can bluff to prevent spectrum usage by asecondary user who suffers from lack of information about the channel gains.The resulting equilibrium can be highly inefficient, suggesting thatcompetitive spectrum sharing is highly suboptimal.
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