Using an evolutionary game, we show that patients and physicians can interact with predator-prey relationships. Litigious patients who seek compensation are the ‘predators’ and physicians are their ‘prey’. Physicians can adapt to the risk of being sued by performing defensive medicine. We find that improvements in clinical safety can increase the share of litigious patients and leave unchanged the share of physicians who perform defensive medicine. This paradoxical result is consistent with increasing trends in malpractice claims in spite of safety improvements, observed for example in empirical studies on anesthesiologists. Perfect cooperation with neither defensive nor litigious behaviors can be the Pareto-optimal solution when it is not a Nash equilibrium, so maximizing social welfare may require government intervention.

Battery energy storage systems (BESS) rely on accurate electricity price forecasts to maximize arbitrage profits in day-ahead markets. We examined whether specific forecasting models, ranging from statistical benchmarks to machine learning methods, consistently deliver superior financial outcomes for storage operators. Using real market data from the Italian day-ahead electricity market over 2020–2024, we compared univariate singular spectrum analysis (SSA), ARIMA, SARIMA, random forests, and a 30-day simple moving average under a unified trading framework. All models were evaluated based on their ability to generate arbitrage profits. Univariate SSA clearly outperformed all alternatives, achieving on average 98% of the theoretical maximum profit while maintaining the lowest forecast error. Among the other models, simpler approaches performed surprisingly well: they achieved comparable, if not superior, profit performance to more complex, hour-specific, or computationally intensive configurations. These results were robust to plausible variations in battery parameters and retraining schedules, suggesting that univariate SSA offers a uniquely effective forecasting solution for battery arbitrage and that simplicity can often be more effective than complexity in operational revenue terms.

Storage profit maximization is based on buying energy at the lowest prices and selling it at the highest prices. The best strategy must thus be based on both accurately predicting the price peak hours and on rightly choosing when to buy and when to sell the stored energy. In this aim, price prediction is crucial, but choosing the prediction model by means of the usual metrics, as the lowest mean squared error, is not an effective solution as the mean squared error computation equally weights the prediction error of all prices, while the focus must be on the higher and lower prices. In this paper, we propose a new metric focused on the correct forecasting of high and low prices so as to allow for a more effective choice among price forecasting models. Results show that the new metric outperforms the standard metrics, allowing for a more accurate estimation of the possible profit for storage (or other trading) activities.