We consider the communication between a source (user) and a destination in the presence of a jammer, and study resource assignment in a non-cooperative game theory framework using communication latency as the user's utility. The user switches between two different modes, i.e., the (a) regular transmission mode, according to which both players follow a Nash equilibrium; and the (b) smart transmission mode, according to which the user always implements the best response strategy. First, we consider the case in which the switching between transmission modes occurs with a given frequency. For this case we find the optimal transmission power of the user by formulating and solving a Bayesian game problem. We show that an increase in the frequency of smart transmissions leads to a decrease in communication latency and to an increase in the total transmission cost. We determine the switching frequency that optimizes the latency-cost trade off using α-fairness criteria. We also discuss the implications of the proposed latency metric on the player strategies as compared to the previously well studied signal-to-interference-plus-noise ratio (SINR) metric.