  In this paper, the fundamental limits of decentralized simultaneous
information and energy transmission in the $K$-user Gaussian multiple access
channel (G-MAC), with an arbitrary $K \geqslant 2$ and one non-colocated energy
harvester (EH), are fully characterized.
  The objective of the transmitters is twofold. First, they aim to reliably
communicate their message indices to the receiver; and second, to harvest
energy at the EH at a rate not less than a minimum rate requirement $b$. The
information rates $R_1,\dots,R_K$, in bits per channel use, are measured at the
receiver and the energy rate $B$ is measured at an EH.
  Stability is considered in the sense of an $\eta$-Nash equilibrium
($\eta$-NE), with $\eta > 0$.
  The main result is a full characterization of the $\eta$-NE
information-energy region, i.e., the set of information-energy rate tuples
$(R_1,\dots,R_K,B)$ that are achievable and stable in the G-MAC when:
  $(a)$ all the transmitters autonomously and independently tune their own
transmit configurations seeking to maximize their own information transmission
rates $R_1,\dots, R_K$; and
  $(b)$ all the transmitters jointly guarantee an energy transmission rate $B$
at the EH, such that $B \geqslant b$.
  Therefore, any rate tuple outside the $\eta$-NE region is not stable as there
always exists at least one transmitter able to increase by at least $\eta$ bits
per channel use its own information transmission rate by updating its own
transmit configuration.
