A combined stochastic NPV and game-theoretic framework for the evaluation of investment decisions in a biogas plant

Biogas plants constitute a viable alternative for achieving both environmental and economic objectives. On the one hand, they address the challenge of waste management within a circular economy framework; on the other, they provide opportunities to generate economic returns through electricity production. Moreover, such facilities offer a profitable option for livestock farmers, who can supply manure to the plant while reducing disposal costs. However, the limited capacity of the plant may give rise to competition among farmers, who may choose whether to supply manure depending on the stochastic evolution of manure flows over time. In this study, we develop a mathematical model grounded in game theory and a stochastic net present value (SNPV) framework, computed through Monte Carlo simulation techniques, to assess the economic benefits for the plant operator and two livestock farmers. We propose a sequential game with three players, in which the plant operator moves first, followed by the two farmers acting as the second and third players, respectively. The Monte Carlo approach is employed to simulate manure flow dynamics at each point in time over the entire project lifecycle.