Game Theory Approach to Design Under Uncertainty

Using some basic concepts from game theory, a framework for the analysis of pollution control investments under uncertainty is developed. Casting the facility designer and nature as the participants in a two-person zero-sum game, and formulating the cost penalties for making incorrect projections as the pay-off matrix, a rational method for determination of the optimal design specification for plant expansions is derived. The relationship between projection uncertainty, interest rates, and scale economies receives particular attention. The method is applied to some recent sewage treatment plant projects, with the results compared to the more traditional design specifications contained in the preliminary design reports. Under the prevailing interest rate conditions, overdesign in the face of flow uncertainty is shown to carry higher economic penalties than underdesign.