$N$-Person Card Game Approach for Solving SET $K$-COVER Problem in Wireless Sensor Networks

Solutions to SET K-COVER problem can prolong the lifetime of wireless sensor networks (WSNs) by partitioning the sensors into sets. In this paper, a novel purely distributed method for solving SET K-COVER problem is introduced based on the game theory, in which we consider the SET K-COVER problem as a noncooperative N-person card game. The sensors in WSN are considered as the players, the cover sets chosen by N sensors are considered as the strategies, and the sensing area covered alone is considered as the payoff function for each sensor. After the gaming process, the best strategies that all of the players have chosen constitute the Nash equilibrium. In addition, we analyze the effects of the initial strategies on the gaming result and propose a solution to avoid this effect in order to obtain a better coverage performance. We also extend the optimality of Nash equilibrium in the coverage game to a more general case. Besides that, the analysis of the convergence performance and the message complexity of the proposed algorithm are also presented. Extensive simulations have been conducted to show the superiority of the proposed algorithm in convergence, robustness, and coverage, comparing with the random, K-COVER, and synchronous Nash equilibria convergence algorithms. Finally, based on the results from real experiments on both small- and large-scale WSNs, we conclude that the proposed algorithm can be applied in real application environment and is also of good performance in both convergence and coverage. Furthermore, we also provide the comparisons between results from simulations and real experiments when some practical issues are considered.