In order to harvest the business potential of device-to-device (D2D)communication, direct communication between devices subscribed to differentmobile operators should be supported. This would also support meetingrequirements resulting from D2D relevant scenarios, like vehicle-to-vehiclecommunication. In this paper, we propose to allocate the multi-operator D2Dcommunication over dedicated cellular spectral resources contributed from bothoperators. Ideally, the operators should negotiate about the amount of spectrumto contribute, without revealing proprietary information to each other and/orto other parties. One possible way to do that is to use the sequence ofoperators' best responses, i.e., the operators make offers about the amount ofspectrum to contribute using a sequential updating procedure until reachingconsensus. Besides spectrum allocation, we need a mode selection scheme for themulti-operator D2D users. We use a stochastic geometry framework to capture theimpact of mode selection on the distribution of D2D users and assess theperformance of the best response iteration algorithm. With the performancemetrics considered in the paper, we show that the best response iteration has aunique Nash equilibrium that can be reached from any initial strategy. Ingeneral, asymmetric operators would contribute unequal amounts of spectrum formulti-operator D2D communication. Provided that the multi-operator D2D densityis not negligible, we show that both operators may experience significantperformance gains as compared to the scheme without spectrum sharing.
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