Sustainable Decisions

Abstract

This paper rigorously defines sustainable decisions from first principles. A decision is sustainable if its performance (e.g., utility) constitutes at least a fair game. From a probabilistic point of view, this idea can be formalized by applying the concept of submartingales. Our approach allows us to establish the novel concept of sustainable optimization and leads to novel sustainable optimization and equilibrium problems. It requires an extension of the classical dynamic-programming paradigm including a formal derivation of a sustainable Bellman principle. Our approach can be applied to a huge number of decision problems where potentially heterogeneous decision makers optimize some form of "well-being" (e.g., utility or costs). We demonstrate its usefulness by studying various problems from economics, finance, marketing, or engineering. We derive sustainable consumption-investment strategies with habit formation or recursive utility, sustainable advertising strategies, sustainable compensation contracts in a principal-agent framework, or a sustainable equilibrium in a two-agent endowment economy.

Keywords: Sustainability, Decision Making, Dynamic Optimization, Heterogeneous Agents

JEL Classification: D15, D82, E21, E23, G11, J11, J22, M37