As an important building block of cognitive radio networks, the interference channel with distributed and competing radio access is currently an active area of research. In this work, a basic two-by-two interference channel is studied by considering random packet arrivals and random access. In particular, each transmitter is assumed to select independently and concurrently a transmission probability based on the state of the system queues. Both the cases of perfect and partial information about the transmitters' backlogs are addressed. The system is analyzed using tools from game theory, and specifically from the theory of stochastic games. The main conclusion is that random packet arrival has a beneficial effect on the efficiency of decentralized random access. This result is achieved by comparing the efficiency of Nash equilibria for the case of backlogged users with the corresponding equilibria in presence of random packet arrivals via numerical simulations.