  We study the problem of decentralized power allocation in a multi-access
channel (MAC) with non-cooperative users, additive noise of arbitrary
distribution and a generalized power constraint, i.e., the transmit power
constraint is modeled by an upper bound on $\mathbb{E}[\phi(|S|)]$, where $S$
is the transmit signal and $\phi(.)$ is some non-negative, increasing and
bounded function. The generalized power constraint captures the notion of power
for different wireless signals such as RF, optical, acoustic, etc. We derive
the optimal power allocation policy when there a large number of
non-cooperative users in the MAC. Further, we show that, once the number of
users in the MAC crosses a finite threshold, the proposed power allocation
policy of all users is optimal and remains invariant irrespective of the actual
number of users. We derive the above results under the condition that the
entropy power of the MAC, $e^{2h(S)+c}$, is strictly convex, where $h(S)$ is
the maximum achievable entropy of the transmit signal and $c$ is a finite
constant corresponding to the entropy of the additive noise.
