In this paper, we investigate two main schemes for contracting demand-side flexibility by the Distribution System Operator (DSO) at the planning stage: a voluntary demand-side connection agreement where consumers offer their flexibility, i.e., load reduction, to the DSO and a mandatory demand-side connection agreement where the DSO sets the flexibility levels, i.e., load curtailment, to be contracted from residential consumers. A different bilevel equilibrium model is used for each demand connection agreement scheme. In both models, the DSO, in the Upper Level, decides on the flexibility price and network tariffs. Residential consumers react to those signals in the Lower Level. They can be prosumers that invest in solar PV and batteries or passive consumers. The paper answers two regulatory issues. The first is which option to choose for regulators between mandatory and voluntary demand connection agreements. We find that mandatory demand-side connection agreements result in higher welfare gains compared to voluntary ones and a lower price for flexibility. However, such agreements may entail some implementation issues for regulators and different curtailment levels among consumers. This connects with the second issue investigated in this paper on how to implement mandatory demand connection agreements from equity and feasibility perspectives. When introducing a pro-rata constrained mandatory scheme, curtailing consumers equally, we find that welfare levels are still higher than under the voluntary scheme but lower than in the unconstrained mandatory scheme. The difference in welfare and flexibility levels between the two mandatory schemes could represent a potential for a secondary flexibility mechanism, where consumers trade flexibility between themselves.