Optimal risk-based levee designs are usually developed for economic efficiency. However, in river systems with multiple levees, the planning and maintenance of different levees are controlled by different agencies or groups. For example, along many rivers, levees on opposite riverbanks constitute a simple leveed river system with each levee designed and controlled separately. Collaborative planning of the two levees can be economically optimal for the whole system. Independent and self-interested landholders on opposite riversides often are willing to separately determine their individual optimal levee plans, resulting in a less efficient leveed river system from an overall society-wide perspective (the tragedy of commons). We apply game theory to simple leveed river system planning where landholders on each riverside independently determine their optimal risk-based levee plans. Outcomes from noncooperative games are analyzed and compared with the overall economically optimal outcome, which minimizes net flood cost system-wide. The system-wide economically optimal solution generally transfers residual flood risk to the lower-valued side of the river, but is often impractical without compensating for flood risk transfer to improve outcomes for all individuals involved. Such compensation can be determined and implemented with landholders' agreements on collaboration to develop an economically optimal plan. By examining iterative multiple-shot noncooperative games with reversible and irreversible decisions, the costs of myopia for the future in making levee planning decisions show the significance of considering the externalities and evolution path of dynamic water resource problems to improve decision-making.