Decentralized channel assignment schemes are proposed to obtain low system-wide spatial overlap regions in wireless local area networks (WLANs). The important point of channel assignment in WLANs is selecting channels with fewer contending stations rather than mitigating interference power due to its medium access control mechanism. This paper designs two potential game-based channel selection schemes, basically each access point (AP) selects a channel with smaller spatial overlaps with other APs. Owing to the property of potential games, each decentralized channel assignment is guaranteed to converge to a Nash equilibrium. In order that each AP selects a channel with smaller overlaps, two metrics are proposed: general overlap-based scheme yields the largest overlap reduction if a sufficient number of stations (STAs) to detect overlaps are available; whereas decomposed overlap-based scheme need not require such STAs, while the performance would be degraded due to the shadowing effect. In addition, the system-wide overlap area is analytically shown to be upper bounded by the negative potential functions, which derives the condition that local overlap reduction by each AP leads to system-wide overlap reduction. The simulation results confirm that the proposed schemes perform better reductions in the system-wide overlap area compared to the conventional interference power-based scheme under the spatially correlated shadowing effect. The experimental results demonstrate that the channel assignment dynamics converge to stable equilibria even in a real environment, particularly when uncontrollable APs exist.

Differential games are considered an extension of optimal control problems, which are used to formulate centralized control problems in smart grids. Optimal control theory is used to study systems consisting of one agent with one objective, whereas differential games are used to formulate systems consisting of multiple agents with multiple objectives. Therefore, a differential-game-theoretic approach is appropriate for formulating decentralized demand-side energy management systems where there are multiple decision-making entities interacting with each other. Moreover, in many smart grid applications, we need to obtain information for control via communication systems. To formulate the influence of communication availability, differential game theory is also promising because the availability of communication is considered as part of an information structure (i.e., feedback or open-loop) in differential games. The feedback information structure is adopted when information for control can be obtained, whereas the open-loop information structure is applied when the information cannot be obtained because of communication failure. This paper proposes a comprehensive framework for evaluating the performance of demand-side actors in a demand-side management system using each control scheme according to both communication availability and sampling frequency. Numerical analysis shows that the proposed comprehensive framework allows for an analysis of trade-off for decentralized and centralized control schemes.