# Wireless Networks under a Backoff Attack: A Game Theoretical Perspective
## 1 Introduction  
The remarkable advances and proliferation in wireless networks in recent years have brought a significant interest in the security and threats to these networks. Specially wireless sensor networks can be the target of many different attacks due to the limited capabilities of the sensors, as some recent surveys show (for instance, [1, 2]). A very important kind of attack addressed to these networks is the backoff attack. It affects to the Medium Access Control (MAC) layer when a CSMA/CA (carrier-sense medium access with collision avoidance) scheme is used to regulate the access to the medium. The backoff mechanism minimizes the risk of collision, i.e., that two or more stations transmit simultaneously, by deferring transmissions during a certain random time period: the backoff window. In a backoff attack, a sensor uses a lower backoff window than the rest of the sensors, thus obtaining a higher throughput at expense of the other sensors [3]. Backoff attacks are a real threat to wireless sensor networks. Firstly, because network adapters are highly programmable [4], thus allowing sensors to modify their backoff parameters. In addition, secondly, because many MAC layer protocols proposed for wireless sensor networks make use of CSMA as medium access mechanism, for instance, SMAC [5], WiseMAC [6], TMAC [7] and DSMAC [8]. Two surveys on MAC layer protocols [9, 10] show that CSMA is the most common access mechanism in contention based MAC protocols. Some studies that treat backoff attacks, such as [11, 12], focus only in the defense mechanism. However, any attack is a conflict between the attacker agents and the defense mechanism. In order to better model this conflict, we will make use of game theory tools: a branch of mathematics used to model conflict. This approach is pretty popular: [13] is a survey on game theory approaches to multiple access situations in wireless networks and [14] is another survey focused on CSMA methods. Two works which study backoff attacks in wireless networks are [4, 15]. We differ from these works in the following points and contributions:* We assume that the defense mechanism lies in a sensor, to which other sensors communicate. We model the conflict individually between each communicating sensor--which can behave normally or attack --and the defending sensor. This is the case of networks with a star topology, in which a central sensor receives the packets of the rest of the network. This topology appears, for instance, in hierarchical routing protocols [16]: in these protocols, the sensors are clustered in order to be energy efficient (one recent example is [17]), each cluster following a star topology. Yet our approach could be adapted to other network topologies (e.g., to a mesh); however, we focus in star topology in this work for simplicity. By differentiating between attacking sensors and the defense sensor, we use a heterogeneous network model: the attacking sensors are greedy and want the maximum individual throughput they can obtain, whereas the defending sensor tries to divide fairly the total throughput among the sensors that communicate with it. This makes our model different from [4; 15]: each sensor may have different interests, which is a more complex and realistic situation. * We use [PERSON]'s model to estimate the total network throughput and use this metric as game payoff: we try to enforce a fair use of the network total throughput. By modeling the total throughput, we contribute to provide a deeper insight on how different parameters influence the fairness of the network. Namely, we will show that fairness is related to the backoff parameters and the number of greedy sensors. * We solve our game both analytically and empirically, proposing a simple algorithm to obtain the game solution, based on regret-matching (RM) algorithm [18]. Our contribution here is twofold: on one side, we provide a theoretical framework to the backoff attack problem, and solve it analytically.