We employ a game theoretic approach to formulate communication between two nodes over a wireless link in the presence of an adversary. We define a constrained, two-player, zero-sum game between a transmitter/receiver pair with adaptive transmission parameters and an adversary with average and maximum power constraints. In this model, the transmitter's goal is to maximize the achievable expected performance of the communication link, defined by a utility function, while the jammer's goal is to minimize the same utility function. Inspired by capacity/rate as a performance measure, we define a general utility function and a payoff matrix which may be applied to a variety of jamming problems. We show the existence of a threshold such that if the jammer's average power exceeds this threshold, the expected payoff of the transmitter at Nash Equilibrium (NE) is the same as the case when the jammer uses its maximum allowable power all the time. We provide analytical and numerical results for transmitter and jammer optimal strategies and a closed form expression for the expected value of the game at the NE. As a special case, we investigate the maximum achievable transmission rate of a rate-adaptive, packetized, wireless AWGN communication link under different jamming scenarios and show that randomization can significantly assist a smart jammer with limited average power.