## 1 Introduction  
After the development of the first four generations, mobile communication systems are encountering new bottlenecks and challenges. On the one hand, many previous hot techniques, such as carrier aggregation, multi-antenna and coordinated multi-point, have been approaching their upper bounds for improving the link-level spectral efficiency [1; 2; 3]. On the other hand, existing network facilities for mobile communications are constructed outdoors, but in-building-generated phone calls and data traffic are expected to account for more than half of the total volume in the near future [4; 5]. To evolve mobile communication systems toward 5G, a new network paradigm has been raised, called heterogeneous cellular networks (HCNs), which is composed of various types of cells deployed complementarily, forming a heterogeneous environment for wireless devices to access [6; 7; 8]. In HCNs, besides macrocells and microcells covering large-scope areas, picocells and femtocells are deployed to cover hotspots and blind zones, so that seamless and ubiquitous access service can be provided at any time anywhere. In the meantime, the Internet of Things (IoT) is also developing rapidly. Applications, such as smart city [9], Internet of vehicles [10], body area network (BAN) [11] and Internet of bio-nano things [12], were extensively studied, making IoT the most promising concept to integrate the Internet with various domains [13], such as industry, agriculture, healthcare, transportation, markets, education, smart homes, _etc._ Dense deployment will be a new and key feature for future wireless communication systems [14]. Recent studies revealed that IoT and HCNs should integrate to form a new wireless network paradigm for providing real-time and always best connected (ABC) services to both sensor and mobile devices [15; 16]. In this network paradigm, mobile devices are able to directly connect to any cell base station (BS) covering it or indirectly connect to a certain BS through a relay. Similarly, sensor devices could also directly transfer data to a BS in the flat networking architecture or indirectly transfer data through a coordinator or relay, such as a mobile device. Figure 1 provides a vision of this network paradigm integrating IoT and HCNs. Seen from each device's point of view, it is intelligent to always select the best cell for access while under the coverage of multiple overlapped cells. Decisions are made distributedly and rationally by devices themselves (or their coordinators) based on terminal properties (such as velocity and battery state), application types (such as bandwidth demand and latency demand) and user preferences (such as monetary cost and security), forming a cell selection (CS) game among a large amount of densely-deployed sensor and mobile devices. Meanwhile, seen from the system's point of view, all of the devices should be associated with their most appropriate cells, so that the whole system performance can be maximized, called CS optimization. Studies on the CS game are limited in the literature, as shown by the related work summary in Section 2. However, studies on a similar topic, called network selection (NS), also called access technology selection, are extensive, including NS using game theory [17; 18; 19; 20; 21]. Various game models have been used, such as the congestion game, evolutionary game and coalition game. In most of these studies, the existence of a pure strategy Nash equilibrium (PSNE) has been proven. Compared to NS, CS is much more complicated due to severe inter-cell interference (ICI) [22, 23]. Unlike heterogeneous access technologies (such as cellular networks and WiFi) using orthogonal spectra, different types of cells in HCNs usually share the same portion of the spectrum for their transmissions. Taking the scenario where a picocell is deployed in a macrocell as an example, devices around the picocell, no matter which cell they finally select, will have interference from adjacent devices selecting the other cell.