In this report, the fundamental limits of decentralized information transmission in the K-user Gaussian multiple access channel (G-MAC), with K>= 2, are fully characterized. Two scenarios are considered. First, a game in which only the transmitters are players is studied. In this game, the transmitters autonomously and independently tune their own transmit configurations seeking to maximize their own information transmission rates, R_1,R_2,...,R_K, respectively. On the other hand, the receiver adopts a fixed receive configuration that is known a priori to the transmitters. The main result consists of the full characterization of the set of rate tuples (R_1,R_2,...,R_K) that are achievable and stable in the G-MAC when stability is considered in the sense of the \eta-Nash equilibrium (NE), with \eta >= 0 arbitrarily small. Second, a sequential game in which the two categories of players (the transmitters and the receiver) play in a given order is presented. For this sequential game, the main result consists of the full characterization of the set of rate tuples (R_1,R_2,\dots,R_K) that are stable in the sense of an \eta-sequential equilibrium, with \eta>= 0.