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We consider a multiple access channel (MAC) problem where several users communicate with a base station and in which the users may have different applications or communication purposes for using the network, which is reflected via associated communication metrics. Specifically, we use throughput as the metric to reflect regular data transmission purposes, and latency, modeled by the inverse throughput, is used to reflect data transmission speed as another metric. The problem is formulated as a non-zero sum game. The equilibrium is derived in closed form. Stability in communication for such a heterogeneous network is established by proving the uniqueness of the equilibrium, except for particular cases where stability still can be maintained via cooperation of users with throughput metric or their switching to latency metric.
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