# Marginal Contribution-Based Distributed Subchannel Allocation in Small Cell Networks
## 1 Introduction
However, the performance guarantee of EPGs comes at the expense of complete information of the environment [8], i.e., decision-makers usually require overall information from other remaining decision-makers in the network [18; 19], making the solution unscalable. To overcome the requirement of global information, we propose the marginal contribution based best-response (MCBR) algorithm of low computational complexity by modeling information exchange requirements only on a specific subchannel of the neighborhood. The main contributions of this paper are summarized as below:  
* For the objective of finding distributed subchannel allocation in SCNs, the concept of MC is utilized to design a welfare-based learning rule for the decision-makers. It is shown that efficient and fair subchannel allocation is achievable in a distributed network if some sort of self-awareness is introduced to decision-makers' learning rules, such that each decision-maker will adapt to improve some measure of the influence caused by its actions to others in the network in addition to improving its own performance. * The welfare-based learning rule maintains the universal properties of an EPG; hence convergence to a pure strategy NE is predictive and guaranteed through best-response (BR) dynamics. Moreover, the proposed MCBR algorithm overcomes the short-comings of EPG for practical implementations in the distributed networks, i.e., complete information of the environment. Here, a decision-maker utilizes the concept of probability distribution in order to select a new subchannel for sensing, and requires information feedback only from those neighboring decision-makers currently using the subchannel. The wireless cellular networks have witnessed an exponential growth in mobile data traffic, mainly due to the popularity of multimedia services and high data rate applications [20]. One of the key emerging trend to accommodate such demand is through network densification, such as extensive deployment of SBSs, by reusing radio resources [21]. Network densification with small cells,which results in spatial densification, has attracted much attention [22; 23; 24] due to its promising network performance with improvement in capacity. Several studies have provided prospects on it from the perspective of key challenges [3; 24; 25], identifying interference management and resource allocation as the most crucial issues that can limit the gains anticipated. The centralized approaches [4; 5; 6; 7] for solving the resource allocation problem in random and dense SCNs are not scalable due to the requirement of global information to manage the le network. On the contrary, convergence speeds of the distributed approaches that require no information exchange [10; 11; 12; 13] are very slow, giving rise to the inherent limitations for practical implementation in large-scale networks with extensive deployment of SBSs. In this work, unlike the traditional opportunistic learning rules in most of the previous studies [14; 15; 16] where each decision-maker acts rationally to maximize their individual performance, we show that implementing the proposed mechanism of the welfare-based learning rule for decision-makers provides network-wide performance improvement with a fair and stable resource allocation solution. Moreover, it is suitable for practical implementation as it requires only local and limited information exchange, which results in low and scalable computational complexity. Recently, the concept of network sharing has also been investigated to allow operators to share their infrastructures in order to maximize the use of existing radio resources while simultaneously minimizing the operational costs [26; 27; 28; 29; 30]. Our work facilitates these recent trends and can be applied as a tool to achieve the much anticipated gains through deployment of small cells by efficient allocation of the radio resources in a distributed fashion.