# Game Algorithm for Resource Allocation Based on Intelligent Gradient in HetNet
## 1 Introduction
This algorithm could be realized through distributed ways and gradually reduce femtocell transmitting power causing strong interference, so as to effectively hinder cross-layer interference. The Stackelberg game is introduced to address numerous problems such as power control [8; 10], but there are only a few algorithms attempted to optimize the spectrum sharing between macro and femtocells. In particular, reference [11] proposed a price based resource allocation strategy to handle the spectrum sharing problem, where the macro base station acts as a leader and protects itself by pricing the interference from femtocell users. In the system model given by [12], the leaders in the Stackelberg game could make priority decisions, while the followers should choose a reasonable resource allocation scheme based on the decisions. Considering both macro base station utility and femtocell utility, reference [14] proposed the Stackelberg game based on an uplink power distribution framework. Under the condition of ensuring Quality of Service (QoS) of macro users, it did not take into account the uplink interference of macro users upon femtocell. Besides, when transmitting power of macro base station was given, the macro base station had enough information to predict response of base station, which would bring large amount of signaling overhead to network. A kind of spectrum leasing framework with one substep to obtain the optimal algorithm of Stackelberg equilibrium was proposed in [16]. Based on the above analysis, a kind of spectrum leasing framework was also proposed in [18], where femtocells lease spectrum from their co-existing macro base stations to serve femtocell users and allow the dynamic access of macro base station users. The above references all assume that each base station in HetNet is an independent individual in game model that attempts to seek maximal energy self-sufficiency without considering the feelings of other individuals in the network, so the optimal overall performance of the community cannot be realized through adjusting self-possessed spectrum resources. Pricing policy considering both economic income and spectrum income was proposed in [19; 20]. When femtocells bought spectrum from a macro base station, the price would be determined by the improvement brought by system throughput. Meanwhile, if femtocellscan provide macro base station users under severe interference with spectrum and access service, the price will be reduced to certain degree. However, setting a spectrum price will lead to high signaling overhead. At the same time, none of the above methods has provided the solution scheme when the value assignment scope for the Nash equilibrium is continuous. The Nash equilibrium is a solution concept of a game involving two or more players in which each player is assumed to know the equilibrium strategies of others, and a player has nothing to gain by just changing their own strategy. Summarizing the results of the above research, some problems exist in current algorithm studies. On the one hand, most algorithms focus on the performance of the macro base station but neglect the performance of the overall system; on the other hand, most of the existing algorithms adopt utility function using earnings to define both game playing parties. Pecuniary transactions are not only impractical but also the cause of high signaling overheads [21]. Moreover, most of the algorithms are Stackelberg game featuring finite discrete perfect information, whose Nash equilibrium solution can be obtained through simple backward induction. However, when the range of participant features have continuum value, game playing will become continuously expansive and dynamic. Equilibrium is never actually reached since the equilibrium they could pick from was discrete. It would drop to the Bertrand equilibrium. Letting the players learn an optimal payoff function, it can be found that automated learning gives consistent results. The optimum for the payoff function corresponds to the optimal price in an equilibrium.