Economic analysis in the context of incomplete knowledge

Abstract

<p>The overall objective of this research is to provide a methodology for determining a complete and final decision line when evaluating a set of mutually exclusive alternatives under the context of incomplete knowledge for both weak and strict ranking;A procedure was developed to search for the extreme variances of payoffs for alternatives under strict ranking. It was proved that the extreme variances under conditions of strict ranking must occur at corner boundary points of the feasible region if more than two distinct payoffs exist for n possible states of nature. If only two distinct payoffs exist for n states of nature, the global maximum of the variance can occur inside the feasible region;The variances and the expected values of payoffs were combined into the index of utility with a coefficient of risk aversion. In order to reduce the chances of unwanted results, a negative coefficient of risk aversion was used to apply heavier penalties for greater variances. An algorithm was developed to search for the extreme indexes of utility under conditions of strict ranking in the context of incomplete knowledge. It was proved that the extreme indexes of utility under conditions of strict ranking must occur at corner boundary points of the feasible region if more than two distinct payoffs exist for n possible states of nature. If only two distinct payoffs exist for n states of nature, the global minimum index of utility can occur inside the feasible region;As the coefficient of risk aversion can be expressed in terms of the minimum attractive rates of return and an angular coefficient, a method of determining the appropriate value of the angular coefficient for a set of mutually exclusive alternative was introduced under the context of uncertainty. This method was then modified and was successfully applied to both the context of uncertainty and the context of risk;The technique of finding the appropriate angular coefficients was then extended to conditions of weak ranking and strict ranking, respectively. After the angular coefficient was determined, it was possible to find the extreme rates of return on index of utility by applying the algorithm of searching for the extreme indexes of utility. A complete and final decision line was then constructed based on the minimum rates of return on index of utility.</p>