Local Criteria for Stable Choice of Power Level

When radiated-power levels are selected for a group of mutually interfering radio stations, it is no longer possible to use the natural criterion for a single channel, the a priori specified signal-to-noise ratio, since independent power control at each transmitter would lead to unstable operation in certain cases. Certain classes of criteria are considered that always provide stable selection of “reasonable” singal-to-noise ratios when local information about the group is available at each transmitter. Existence and uniqueness are proven for Nash plays in games involving automata with continuous sets of moves corresponding to these criteria.