Savage's Vision in Decision-Making, Models and Algorithms

Abstract

In the context of solving applied economic problems, uncertainty generally generates a multitude of decision-making difficulties. These require specification based on the type of the decision-maker, the environment, available resources and decision constraints as well as other factors. This article looks at one specific sequence from this multitude - namely - the one that refers to the regret criterion, known in the literature as Savage's criterion. It is important to clarify from the beginning that the number of states of nature is considered finite, the admissible decision domain is a compact and convex set in the corresponding space, and the functions generated by all states of nature - which in this case represent costs - are considered convex and continuous over the given decision domain. Evaluating the regret for each state of nature is, in itself, a difficult problem. Estimating the values of the Savage function for any specific decision option is even more challenging. This paper proposes a method for minimizing Savage’s regret function, which is developed based on the well-known generalized gradient projection method. This proposed method can be implemented in multiple versions depending on the number of states of nature, the number of constraints that define the admissible decision domain as well as other factors and limitations. All these versions are implemented through specific algorithms. The convergence conditions of the algorithms are established and the application areas for these numerical schemes are indicated. The identification of sectors of the economy where the developed algorithms could be tested from various perspectives represents a particular interest in the context of this research. JEL: C61, C63, D81