## 1 Introduction  
Wireless sensor networks (WSNs) are composed of many tiny devices, each with sensing and data storing, processing and communication capabilities. Sensor networks have many potential applications, such as battlefield surveillance, environmental monitoring and industrial asset management. However, the design of energy efficient, scalable routing algorithms remains a challenging issue for researchers. Recently, some research efforts have focused on establishing efficient routing paths for transmitting packets from a sensor node to a sink in wireless sensor networks [1]. Shortening the route length can help reduce the transmission overhead and delay time, as well as increase the packet delivery ratio. However, the existence of obstacles may either impede the establishment of a routing path or increase the route length. Generally, any geographic region where sensing and communication are not possible can be treated as an obstacle. In wireless sensor networks, obstacles can be formed dynamically owing to several reasons [2]: firstly, the random deployment of sensors can causes a non-uniform distribution of wireless sensor networks, where some regions might not contain any sensor nodes. Secondly, some sensor nodes exhaust their power after working for a relatively long period of time, resulting in regions without any sensing and communication functionality. Thirdly, physical obstacles such as mountains or buildings may also be encountered. Fourthly, sensor nodes in some regions may not work normally owing to malicious signal interference. Finally, passing groups of animals or a strong breeze blowing on the sensor networks can also cause some sensor nodes to fail or be swept away, dynamically forming an obstacle. Once obstacles appear, packet routing will be blocked or become inefficient. In the absence of any appropriate obstacle avoidance routing technique, this would lead to a situation where packets may get lost in the network, wasting node energy and disabling communications between some node pairs. Existing obstacle handling techniques mainly use the following two approaches to solve the problem: the right hand rule [3] and the backpressure rule [4]. Some recent protocols are also based on the right hand rule-bypass packets to the sink approach [5,6]. According to the right hand rule, packets tend to be forwarded along the boundaries of obstacles. The probability that the obstacle boundary nodes are then shared by several communication sessions is higher than for other nodes. This results in excessive energy consumption and data collisions within these nodes. In [7], an anchor node is proposed to solve the routing problem with obstacles in sensor networks. This approach can mitigate excessive energy consumption and reduce the collision of boundary nodes, since packets would be forwarded through anchor-based virtual circles. However, the obstacle diffusion issue still occurs in the network initialization phase. In this paper, we propose a novel protocol to handle the obstacle problem based on forwarding mechanisms in sensor networks. Our protocol first computes the connectivity degree set for every node and separates the degree set into out-degree and in-degree sets. Given that some nodes may have zero out-degree, we establish a concave region in the sensor network. Packets cannot be forwarded to the concave region and this approach can avoid lost packets and reduce the transmission delay. Secondly, during the phase of forwarding node selection of source nodes, the source node considers residual energy, out-degree and forwarding angle of forwarding candidates and infers the forwarding probability according to these three factors. Furthermore, we provide a game theory model based onthe forwarding probability of forwarding participants and prove that in the game model a Nash equilibrium exists. The rest of this paper is organized as follows: Section 2 presents related works on obstacle based routing and game theory-based protocols in wireless sensor networks.