We provide a novel distributed non-substitution matching scheme for matching game instead of classic substitution scheme.
In this section, we give a brief review of the related works on cooperative communication and some related applications of matching game theory in wireless networks.
Matching game theory has recently attracted a lot of attention in wireless networks, such as cell association [18-21] and cooperative spectrum sharing [22, 23].
Definition 1 : A two-sided matching game is defined by two sets of players (M,N) and two preference relations [?
In the matching game theory, such problems are defined as peer effects .
There is a need to develop new algorithms that significantly differ from existing applications of matching theory in wireless such as [18-23], so as to find the solutions of the studied many-to-one matching game.
Matching Game for Aggregate Throughput Optimization
For the application of matching game in wireless network models, the classic DA algorithm  has been adopted or improved to solve selection problems in some literatures [18, 20, 26].
Matching Game for Fairness Optimization and Non-Substitution Model
In the classic matching game model, two-sided players will only strictly accept the best strategies for their own, the trait of which is alternative.
We define this situation as non-substitution preference of matching game model.
For fairness optimization, we pointed out that the conventional models of matching game are alternative models and not suitable for some practical network systems.