Caching in wireless device-to-device (D2D) networks can be utilized to offload data traffic during peak times. However, the design of incentive mechanisms is challenging due to the heterogeneous preference and selfish nature of user terminals (UTs). In this paper, we propose an incentive mechanism in which the base station (BS) rewards those UTs that share contents with others using D2D communication. We study the cost minimization problem for the BS and the utility maximization problem for

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... UT. In particular, the BS determines the rewarding policy to minimize his total cost, while each UT aims to maximize his utility by choosing his caching policy. We formulate the conflict among UTs and the tension between the BS and the UTs as a Stackelberg game. We show the existence of the equilibrium and propose an iterative gradient algorithm (IGA) to obtain the Stackelberg Equilibrium. Extensive simulations are carried out to evaluate the performance of the proposed caching scheme and comparisons are drawn with several baseline caching schemes with no incentives. Numerical results show that the caching scheme under our incentive mechanism outperforms other schemes in terms of the BS serving cost and the utilities of the UTs.