With increasing decarbonisation and accessibility to our energy systems and markets, there is a need to understand and optimise the value proposition for different stakeholders. Game-theoretic models represent a promising approach to study strategic interactions between self-interested private energy system investors. In this work, we design and evaluate a game-theoretic framework to study strategic interactions between profit-maximising players that invest in network, renewable generation and storage capacity. Specifically, we study the case where grid capacity is developed by a private renewable investor, but line access is shared with competing renewable and storage investors, thus enabling them to export energy and access electricity demand. We model the problem of deducing how much capacity each player should build as a non-cooperative Stackelberg-Cournot game between a dominant player (leader) who builds the power line and renewable generation capacity, and local renewable and storage investors (multiple followers), who react to the installation of the line by increasing their own capacity. Using data-driven analysis and simulations, we developed an empirical search method for estimating the game equilibrium, where the payoffs capture the realistic operation and control of the energy system under study. A practical demonstration of the underlying methodology is shown for a real-world grid reinforcement project in the UK. The methodology provides a realistic mechanism to analyse investor decision-making and investigate feasible tariffs that encourage distributed renewable investment, with sharing of grid access.