Spectrum sharing between multiple independent, coexisting transmit-receive pairs (TRPs, also termed as users) is formulated as a non-cooperative game with the TRPs as players, their individual link rates as payoffs and the iterative water-filling algorithm (IWFA) as the strategy for each TRP. The dynamics of this distributed algorithm are studied for sequential and simultaneous update mechanisms to determine the nature of convergence. Global convergence to unique Nash Equilibrium (NE) is considered and sufficient conditions tighter than those in the literature are derived. Necessary conditions are also derived to complement the sufficient conditions. The necessary conditions serve as tools for characterizing the structure of NE and also highlight the sensitivity of convergence to update orders in sequential IWFA.