  We study the fundamental problem of distributed network formation among
mobile agents of limited computational power that aim to achieve energy balance
by wirelessly transmitting and receiving energy in a peer-to-peer manner.
Specifically, we design simple distributed protocols consisting of a small
number of states and interaction rules for the formation of arbitrary and k-ary
tree networks. Furthermore, we evaluate (theoretically and also using computer
simulations) a plethora of energy redistribution protocols that exploit
different levels of knowledge in order to achieve desired energy distributions
among the agents which require that every agent has exactly or at least twice
the energy of the agents of higher depth, according to the structure of the
network. Our study shows that without using any knowledge about the network
structure, such energy distributions cannot be achieved in a timely manner,
meaning that there might be high energy loss during the redistribution process.
On the other hand, only a few extra bits of information seem to be enough to
guarantee quick convergence to energy distributions that satisfy particular
properties, yielding low energy loss.
