Mandatory pension systems only partially replace old-age income, therefore the government operates a voluntary pension system, where savings are matched by government grants (OECD, 2005). The literature generally neglects the resulting tax expenditure and the resulting perverse redistribution from the shortsighted to farsighted workers (for an exception, see Simonovits, 2011).  The present models break down the accumulation process, leaving room for dynamic learning by the shortsighted types.  Our analytical model serves as a starting point for analyzing more complex and realistic learning in an agent-based framework. Joint with Balázs Király.