  In wireless access network optimization, today's main challenges reside in
traffic offload and in the improvement of both capacity and coverage networks.
The operators are interested in solving their localized coverage and capacity
problems in areas where the macro network signal is not able to serve the
demand for mobile data. Thus, the major issue for operators is to find the best
solution at reasonable expanses. The femto cell seems to be the answer to this
problematic. In this work (This work is supported by the COMET project AWARE.
http://www.ftw.at/news/project-start-for-aware-ftw), we focus on the problem of
sharing femto access between a same mobile operator's customers. This problem
can be modeled as a game where service requesters customers (SRCs) and service
providers customers (SPCs) are the players.
  This work addresses the sharing femto access problem considering only one SPC
using game theory tools. We consider that SRCs are static and have some similar
and regular connection behavior. We also note that the SPC and each SRC have a
software embedded respectively on its femto access, user equipment (UE).
  After each connection requested by a SRC, its software will learn the
strategy increasing its gain knowing that no information about the other SRCs
strategies is given. The following article presents a distributed learning
algorithm with incomplete information running in SRCs software. We will then
answer the following questions for a game with $N$ SRCs and one SPC: how many
connections are necessary for each SRC in order to learn the strategy
maximizing its gain? Does this algorithm converge to a stable state? If yes,
does this state a Nash Equilibrium and is there any way to optimize the
learning process duration time triggered by SRCs software?
