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Wireless Heterogeneous Sensor Network (WHSN) facilitates ubiquitous information acquisition for Ambient Intelligence (AmI) systems. It is of great importance of power management and topology control for WHSN to achieve desirable network performances, such as clustering properties, connectivity and power efficiency. This paper proposes a game theoretic model of topology control to analyze the decentralized interactions among heterogeneous sensors. We study the utility function for nodes to achieve desirable frame success rate and node degree, while minimizing the power consumption. Specifically, we propose a static complete-information game formulation for power scheduling and then prove the existence of the Nash equilibrium with simultaneous move. Because the heterogeneous sensors typically react to neighboring environment based on local information and the states of sensors are evolving over time, the power-scheduling problem in WHSN is further formulated into a more realistic incomplete-information dynamic game model with sequential move. We then analyze the separating equilibrium, one of the perfect Bayesian equilibriums resulted from the dynamic game, with the sensors revealing their operational states from their actions. The sufficient and necessary conditions for the existence of separating equilibrium are derived for the dynamic Bayesian game, which provide theoretical basis to the proposed power scheduling algorithms, NEPow and BEPow. The primary contributions of this paper include applying game theory to analyze the distributed decision-making process of individual sensor nodes and to analyze the desirable utilities of heterogeneous sensor nodes. Simulations are presented to validate the proposed algorithms and the results show their ability of maintaining reliable connectivity, reducing power consumption, while achieving desirable network performances.
Ren et al. (Wed,) studied this question.