Game Theory and Risk-Based Levee System Design

Abstract:

Risk-based analysis has been developed for optimal levee design for economic efficiency. Along many rivers, two levees on opposite riverbanks act as a simple levee system. Being rational and self-interested, land owners on each river bank would tend to independently optimize their levees with risk-based analysis, resulting in a Pareto-inefficient levee system design from the social planner’s perspective. Game theory is applied in this study to analyze decision making process in a simple levee system in which the land owners on each river bank develop their design strategies using risk-based economic optimization. For each land owner, the annual expected total cost includes expected annual damage cost and annualized construction cost. The non-cooperative Nash equilibrium is identified and compared to the social planner’s optimal distribution of flood risk and damage cost throughout the system which results in the minimum total flood cost for the system. The social planner’s optimal solution is not feasible without appropriate level of compensation for the transferred flood risk to guarantee and improve conditions for all parties. Therefore, cooperative game theory is then employed to develop an economically optimal design that can be implemented in practice. By examining the game in the reversible and irreversible decision making modes, the cost of decision making myopia is calculated to underline the significance of considering the externalities and evolution path of dynamic water resource problems for optimal decision making.