The multiple-access collision channel without feedback: Capacity region and a mutual information game

This paper revisits the collision channel without feedback by reformulating it as a deterministic multiple-access channel. The capacity region of this channel is computed for different cardinalities of the input alphabets, and it is shown that: for alphabets with small cardinalities, the users exploit the action of transmitting vs. not transmitting to communicate at rates on the boundary of the capacity region; and as the alphabet cardinalities increase, the time-sharing inner bound approaches the boundary of the capacity region. A non-cooperative mutual information game is also considered and the existence of a unique Nash-equilibrium solution is established.