Evolutionary dynamics of interdependent exogenous risks

Any significant decision making process involves dealing with many complexities including spatial interactions, temporal changes, interdependencies between system components and risk and uncertainties associated with decision choices. In this paper, we attempt to capture part of these complexities using an evolutionary game theoretic framework. At the heart of this framework is a game called InterDependent Security (IDS). In IDS games players opt between investing or not investing in securing themselves against possible losses in case of a negative risk event. Two models of IDS games are considered where both investors and non-investors share the risk of loss from a bad event. In the first model, the occurrence of a risk event is of a given probability and the players receive payoffs based on the expected loss. In the second model, events are modelled as stochastic processes and the game dynamics are studied in multi-period encounters. Game dynamics for both of these models are investigated over a range of cost to loss ratios under different levels of exogenous risk. The spatial effects are captured by placing the player population on a regular graph, and the evolutionary dynamics are modelled through a best-takeover update rule. There are significant differences between the dynamics of the two IDS models. The simulation results for deterministic model show three equilibrium regimes which conform to the conditions derived analytically. Stochastic games, on the other hand, show only two stable states for the most part of the parametric range. These states alternate cyclically throughout the iterations of the game.