A sensor node (SN) in Wireless Sensor Networks (WSNs) can decide whether to collaborate with others based on a trust management system (TMS) by making a trust decision. In this paper, we study the trust decision and its dynamics that play a key role to stabilize the whole network using evolutionary game theory. When SNs are making their decisions to select action Trust or Mistrust, a WSNs trust game is created to reflect their utilities. An incentive mechanism bound with one SN's trust degree is incorporated into this trust game and effectively promotes SNs to select action Trust. The replicator dynamics of SNs' trust evolution, illustrating the evolutionary process of SNs selecting their actions, are given. We then propose and prove the theorems indicating that evolutionarily stable strategies can be attained under different parameter values, which supply theoretical foundations to devise a TMS for WSNs. Moreover, we can find out the conditions that will lead SNs to choose action Trust as their final behavior. In this manner, we can assure WSNs' security and stability by introducing a trust mechanism to satisfy these conditions. Experimental results have confirmed the proposed theorems and the effects of the incentive mechanism.
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