Game theory is a promising approach for the system-level analysis of power control (PC) in wireless networks. This paper extends game-theoretic analysis to the study of link adaptation, which involves the variation of modulation parameters, in addition to PC. We use the link adaptation scheme in general packet radio service (GPRS) as an example, although the basic approach is applicable to any centralized wireless system with power and rate control. The action space of a player in our proposed game, which is called the link adaptation game (LAG), consists of power, as usual, and a discrete-valued adaptable link parameter (ALP), e.g., code rate. The utility function is a sigmoid (which is fitted to the throughput characteristics of a link adaptation scheme) priced by the square of power. We first show the existence of a Nash equilibrium (NE) in the game. Next, we propose a distributed algorithm to discover the NE. The algorithm is analytically shown to converge to an NE by treating it as a point-to-set map. Simulation results using the GPRS system demonstrate superior throughput and fair system-wide allocation of resources in comparison with other non game-theoretic methods.