A dual purpose communication and radar system is considered, operating in the presence of a jammer. The system transmits communication signals and uses their reflections off targets to support target tracking. A game theoretic framework is used to design the system, i.e., determine power allocations, so that the performance of both communication and radar components is optimized. Two metrics are considered and compared for system design: (a) a weighted combination of signal-to-interference-plus-noise ratio (SINR) of the communication and radar components, reflecting the performance of both components; and (b) a weighted combination of the inverse SINRs of the corresponding components, reflecting the latency in the performance of the components. The comparison suggests that the latency metric enables a design that requires less a priori information on fading gains, and further, as the decision rule can be derived in closed form, the design is easier implementable in practice. The interaction between the system and the jammer is modeled by non-zero sum games. A Bayesian extension of the games allows us to investigate the impact that incomplete information about the underlying network parameters has upon the strategies that should be employed.