This paper presents a novel transport network design approach that incorporates supply- and demand-side factors and emphasises equity as a key objective. The proposed model introduces a planning agency as the dominant player responsible for strategic decision-making to regulate the market and influence the behaviours of other participants. The paper addresses the complex dynamics between the planning agency and other players by formulating and solving a Stackelberg game within a network-constrained transport system. The proposed formulation is a mathematical program with equilibrium constraints (MPEC) which can capture this interaction effectively. The MPEC is reformulated as a mixed-integer linear program (MILP) to solve the model by employing disjunctive constraints. To demonstrate the model's capabilities for policy analysis, we conduct numerical experiments on a toy network in Sydney. The computational models developed in this study provide insights into the impacts of different network designs on important aspects of transport systems, including equality in subsidy distribution, toll collection, and modal share among different user groups.