A bilevel approach to multi-period natural gas pricing and investment in gas-consuming infrastructure

This paper investigates the strategic pricing behavior of a leader in a two-person, noncooperative game when profits depend on the purchasing response of a follower who not only reacts to changing prices instantaneously, but also builds long-lived consumption infrastructure that affects future demand. As an application of such a system, we formulate the relationship between these players in the natural gas and electricity generation industries as a bilevel problem. The leader is a natural gas producer whose objective is to maximize profit; the follower is an electric utility who solves a capacity expansion and dispatch problem with the objective of minimizing the cost of electricity generation and long-run investments. To find solutions, the bilevel problem is reformulated as a mixed-integer linear program by replacing the lower-level player's model with its Karush- Kuhn-Tucker conditions, which are necessary and sufficient for optimality here, and linearizing the upper-level player's objective function using the strong duality conditions of the lower-level problem. After parameterizing the model with publicly available data for Texas, we conduct scenario analyses through 2040, evaluating strategies of the natural gas producer under different policies regarding carbon taxes and incentives for carbon capture and storage (CCS). We then observe how the lower-level player responds to these strategies in terms of the evolution of the generation mix, added capacity, and CO 2 emissions. We also quantify the effects of strategic pricing by running scenarios where natural gas prices are fixed. Key findings include: (1) different levels of carbon tax and CCS incentive can have non-monotonic effects on the optimal natural gas price and producer profit, (2) effects of CCS incentives can spill over to technologies without CCS, and (3) omission of strategic pricing from the model not only decreases the profit for the producer but also can increase the costs for the electricity sector.