Wireless networks are increasingly moving towards a heterogeneous operating model involving the sharing of spectrum resources by different access technologies. Sharing wireless resources between different wireless technologies requires protocols that share spectrum in an equitable manner. In this paper, we examine the time-sharing of wireless channels by Wi-Fi and LTE-U networks. To design fair access protocol for the networks we use $$\alpha $$ fairness criterion. It allows to find a continuum of fair protocols (a protocol per $$\alpha $$). To find the most fair from this continuum of fair protocols we apply Nash bargaining approach. In particular, we show that such a time-sharing bargaining protocol, in spite of the interference between signals, can lead to a gain for both networks under an increase of the transmission power to one of them.