RESUMEN
Decreasing costs of distributed generation and storage, alongside increasing network charges, provide consumers with a growing incentive to defect from the main grid. On a large scale, this may lead to price inflation, hindrance of the energy transition, and even a "death spiral" - a domino effect of disconnections. Here, we develop a game-theoretic framework that demonstrates how conflicting interests among consumers - an aspect that previous studies overlooked - may lead to complex dynamics of grid defection. Our results reveal that although individual consumers benefit from staying connected at the distribution level, the defection of small energy communities from the grid may lead to the defection of larger communities. We also demonstrate that centralized design approaches may lead to inefficient outcomes, e.g., redundant grid expansions, because of the inherent inability to predict potential defections. However, we indicate how, by properly incorporating defection considerations into the grid's design, social welfare can be improved.
RESUMEN
The ribosome flow model (RFM) is a phenomenological model for the flow of particles along a one-dimensional chain of n sites. It has been extensively used to study ribosome flow along the mRNA molecule during translation. When the transition rates along the chain are time-varying and jointly T-periodic the RFM entrains, i.e. every trajectory of the RFM converges to a unique T-periodic solution that depends on the transition rates, but not on the initial condition. In general, entrainment to periodic excitations like the 24 h solar day or the 50 Hz frequency of the electric grid is important in numerous natural and artificial systems. An interesting question, called the gain of entrainment (GOE) in the RFM, is whether proper coordination of the periodic translation rates along the mRNA can lead to a larger average protein production rate. Analysing the GOE in the RFM is non-trivial and partial results exist only for the RFM with dimensions n = 1, 2. We use a new approach to derive several results on the GOE in the general n-dimensional RFM. Perhaps surprisingly, we rigorously characterize several cases where there is no GOE, so to maximize the average production rate in these cases, the best choice is to use constant transition rates all along the chain.