In social interactions, including cooperation and conflict, individuals can adjust their behaviour over the shorter term through learning within a generation, and natural selection can change behaviour over the longer term of many generations. Here we investigate the evolution of cognitive bias by individuals investing into a project that delivers joint benefits. For members of a group that learn how much to invest using the costs and benefits they experience in repeated interactions, we show that overestimation of the cost of investing can evolve. The bias causes individuals to invest less into the project. Our explanation is that learning responds to immediate rather than longer-term rewards. There are thus cognitive limitations in learning, which can be seen as bounded rationality. Over a time horizon of several rounds of interaction, individuals respond to each other's investments, for instance by partially compensating for another's shortfall. However, learning individuals fail to strategically take into account that social partners respond in this way. Learning instead converges to a one-shot Nash equilibrium of a game with perceived rewards as payoffs. Evolution of bias can then compensate for the cognitive limitations of learning.