A growing number of experimental and theoretical studies show the importance of partner choice as a mechanism to promote the evolution of cooperation, especially in humans. In this paper, we focus on the question of the precise quantitative level of cooperation that should evolve under this mechanism. When individuals compete to be chosen by others, their level of investment in cooperation evolves towards higher values, a process called competitive altruism, or runaway cooperation. Using a classic adaptive dynamics model, we first show that, when the cost of changing partner is low, this runaway process can lead to a profitless escalation of cooperation. In the extreme, when partner choice is entirely frictionless, cooperation even increases up to a level where its cost entirely cancels out its benefit. That is, at evolutionary equilibrium, individuals gain the same payoff than if they had not cooperated at all. Second, importing models from matching theory in economics we, however, show that, when individuals can plastically modulate their choosiness in function of their own cooperation level, partner choice stops being a runaway competition to outbid others, and becomes a competition to form the most optimal partnerships. In this case, when the cost of changing partner tends toward zero, partner choice leads to the evolution of the socially optimum level of cooperation. This last result could explain the observation that human cooperation seems to be often constrained by considerations of social efficiency.