Calculus of Power Real Options in the Dynamics of Political Regimes

This paper develops a real options–based framework for modeling the dynamics of political regimes, integrating decision theory with a six-state Markov Decision Process (MDP). Political regimes are treated as strategic decision-makers holding flexible political options—such as repression, reform, policy shift, or exit—whose value evolves with volatility, entropy, and time. The core asset is the regime’s political capital, modeled as a dynamic stock S(t) subject to both gradual diffusion and sudden Poisson jumps representing exogenous shocks (e.g., coups, assassinations, natural death). Option exercise is constrained by an Action Cost Threshold X(t), the political strike price, which evolves over time and determines the cost–benefit feasibility of action.The framework introduces novel visualization and diagnostic tools: Opportunity Landscapes to map option exercise probabilities over volatility and time; Valence of Power heatmaps to measure relative option value; Decision Thresholds under Uncertainty curves linking entropy and action probabilities to reveal points of strategic equivalence; and Volatility Landscapes that integrate volatility, entropy, and probability to assess stability risk. We model the Decay Time Value of Political Capital Stocks and Political Options, quantify the Time Evolution of both S(t) and X(t), and use Cost–Benefit Landscapes to jointly evaluate capital and cost trajectories. The framework also captures coercion dynamics, distinguishing between rational coercion in dysfunctional equilibria and irrational coercion in stable democracies.Applied to Rwanda, South Sudan, and Uganda, the model produces empirical simulations of resilience, fragility, and optimal decision timing. In addition to capturing volatility and cost thresholds, the analysis introduces Regime Survivability Probabilities—quantifying the joint likelihood of sustaining or losing power under affordability and hazard constraints—and the Regime Survivability Frontier, which traces the tipping points where survival and failure probabilities converge. Results show how shifting volatility, erosion of political capital, and rising exit hazards shape strategic urgency and force leaders toward difficult trade-offs. The approach offers a predictive and diagnostic tool for political survival analysis, grounded in the theory of real options but adapted to the contingencies of political power.