Theoretical studies have shown that cooperation tends to evolve when interacting individuals have positively correlated phenotypes. In the present article, we explore the situation where this correlation results from information exchange between social partners, and behavioral flexibility. We consider the game 'continuous iterated prisoner's dilemma'. The level of cooperation expressed by individuals in this game, together with their ability to respond to one another, both evolve as two aspects of their behavioral strategy. The conditions for a strategy to be evolutionarily stable in this game are degenerate, and earlier works were thus unable to find a single ESS. However, a detailed invasion analysis, together with the study of evolution in finite populations, reveals that natural selection favors strategies whereby individuals respond to their opponent's actions in a perfectly mirrored (i.e., correlated) fashion. As a corollary, the overall payoff of social interactions (i.e., the amount of cooperation) is maximized because couples of correlated partners effectively become the units of selection.