Present-biased optimization

Abstract

This paper explores the behavior of present-biased agents, that is, agents who erroneously anticipate the costs of future actions compared to their real costs. Specifically, we extend the original framework proposed by Akerlof (1991) for studying various aspects of human behavior related to time-inconsistent planning, including procrastination, and abandonment, as well as the elegant graph-theoretic model encapsulating this framework recently proposed by Kleinberg and Oren (2014). The benefit of this extension is twofold. First, it enables to perform fine-grained analysis of the behavior of present-biased agents depending on the optimization task they have to perform. In particular, we study covering tasks vs. hitting tasks and show that the ratio between the cost of the solutions computed by present-biased agents and the cost of the optimal solutions may differ significantly depending on the problem constraints. Second, it enables us to study not only the underestimation of future costs, coupled with minimization problems, but also all combinations of minimization/maximization, and underestimation/overestimation. We study the four scenarios, and establish upper bounds on the cost ratio for three of them (the cost ratio for the original scenario was known to be unbounded), providing a complete global picture of the behavior of present-biased agents, as far as optimization tasks are concerned.