In this paper, 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 transmission rates, R_1,..., 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_K) that are achievable and stable in the G-MAC when stability is considered in the sense of the η-Nash equilibrium (NE), with η>=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_K) that are stable in the sense of an η-sequential equilibrium, with η>=0 arbitrarily small.