Mandatory pension systems only partially replace old-age income, therefore the government also operates a voluntary pension system, where savings are matched by government grants. Accounting for the resulting tax expenditure, our models describe the income flow from shortsighted to farsighted workers. 1. In rational models, explicit results are obtained, showing the limited learning of shortsighted workers. 2. In agent-based models, this learning is improved and this raises the shortsighted workers' saving and reduces perverse income redistribution.