Optimistic responsiveness -- the ability of a consensus protocol to operate at the speed of the network -- is widely used in consensus protocol design to optimize latency and throughput. However, blockchain applications incentivize validators to play timing games by strategically delaying their proposals, since increased block time correlates with greater rewards. Consequently, it may appear that responsiveness (even under optimistic conditions) is impossible in blockchain protocols. In this work, we develop a model of timing games in responsive consensus protocols and find a prisoner's dilemma structure, where cooperation (proposing promptly) is in the validators' best interest, but individual incentives encourage validators to delay proposals selfishly. To attain desirable equilibria, we introduce dynamic block rewards that decrease with round time to explicitly incentivize faster proposals. Delays are measured through a voting mechanism, where other validators vote on the current leader's round time. By carefully setting the protocol parameters, the voting mechanism allows validators to coordinate and reach the cooperative equilibrium, benefiting all through a higher rate-of-reward. Thus, instead of responsiveness being an unattainable property due to timing games, we show that responsiveness itself can promote faster block proposals. One consequence of moving from a static to dynamic block reward is that validator utilities become more sensitive to latency, worsening the gap between the best- and worst-connected validators. Our analysis shows, however, that this effect is minor in both theoretical latency models and simulations based on real-world networks.