  In this paper, we enable the coexistence of multiple wireless body area
networks (BANs) using a finite repeated non-cooperative game for transmit power
control. With no coordination amongst these personal sensor networks, the
proposed game maximizes each network's packet delivery ratio (PDR) at low
transmit power. In this context we provide a novel utility function, which
gives reduced benefit to players with higher transmission power, and a
subsequent reduction in radio interference to other coexisting BANs.
Considering the purpose of inter-BAN interference mitigation, PDR is expressed
as a compressed exponential function of inverse
signal-to-interference-and-noise ratio (SINR), so it is essentially a function
of transmit powers of all coexisting BANs. It is shown that a unique Nash
Equilibrium (NE) exists, and hence there is a subgame-perfect equilibrium,
considering best-response at each stage independent of history. In addition,
the NE is proven to be the socially optimal solution across all action
profiles. Realistic and extensive on- and inter-body channel models are
employed. Results confirm the effectiveness of the proposed scheme in better
interference management, greater reliability and reduced transmit power, when
compared with other schemes that can be applied in BANs.
