Jamming Game in a Dynamic Slotted ALOHA Network

In this paper we suggest a development of the channel capacity concept for a dynamic slotted ALOHA network. Our object is to find maxmin successful transmissions of an information over a dynamic communication channel. To do so, we analyze an ALOHA-type medium access control protocol performance in the presence of a jammer. The time is slotted and the system is described as a zero-sum multistage matrix game. Each player, the sender and the jammer, have different costs for respectively sending their packets and jamming, and the jammer wants to minimize the payoff function of the sender. For this case, we found explicit expression of the equilibrium strategies depending on the costs for sending packets and jamming. Properties of the equilibrium are investigated. In particular we have found a simple linear correlation between the probabilities to act for both players in different channel states which are independent on the number of packets left to send. This relation implies that increasing activity of the jammer leads to reducing activity of the user at each channel state. The obtained results are generalized for the case where the channel can be in different states and change according to a Markov rule. Numerical illustrations are performed.