WANG Guocheng, WANG Long
Uncertainty is ubiquitous in natural and engineered systems, influencing both individual decisions and collective dynamics. While robust control theory has provided powerful tools for analyzing how uncertainty affects engineered systems, the study of robustness in game theory remains limited. This paper introduces three fundamental models to capture distinct sources of uncertainty: Environmental stochasticity affecting the payoff structure, demographic fluctuations arising from stochastic reproduction, and perceptual uncertainty shaped by noisy observation and subjective risk preference, extending the concept of robustness to strategic and evolutionary systems. Together, these models reveal how uncertainty at different levels-external, internal, and cognitive-can reshape evolutionary outcomes, alter stability, and generate complex dynamical patterns such as coexistence, multistability, and oscillations. Based on these theoretical foundations, the authors further study the evolution of cooperation in variable-sized populations with mutation. The analysis shows that when the population is divided into multiple subpopulations, migration among subgroups can effectively protect cooperators from the invasion of defectors and sustain cooperation even under mutation. This result demonstrates how robustness concepts can elucidate the emergence and persistence of cooperation in uncertain and heterogeneous environments.
