The Sethi-Skiba point: a structural taxonomy of threshold phenomena in dynamic management problems

Nonconvex dynamic optimisation problems often admit multiple locally optimal outcomes, requiring decision makers to choose not only how to adjust but which equilibrium to pursue. The Sethi-Skiba point identifies the threshold state where a decision maker is indifferent between trajectories leading to radically different regimes. While well-known in control theory, its implications for management science remain fragmented. This paper provides a unified review of the theory, computation, and applications of Sethi-Skiba thresholds. We present geometric foundations in capital accumulation models, explaining connections to nonconcave value functions, hysteresis, and global optimality. We then survey numerical methods and their high-dimensional limitations. Building on this, we organise the literature into a taxonomy of managerial archetypes: Revitalisation, Preservation, Social Trap, and Innovation. Identical mathematical structures govern problems in advertising, environmental management, epidemics, and industrial competition. By reframing Sethi-Skiba points as a general theory of strategic thresholds, this review highlights a shift from marginal adjustment to basin selection. Managerial success in nonconvex environments depends less on fine-tuning controls than on correctly identifying regime boundaries. We conclude by outlining directions in behavioural modelling, empirical detection of tipping points, and networked systems.