  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, the paper extends 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 optimisation 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, our extension enables to study not only
underestimation of future costs, coupled with minimization problems, but also
all combinations of minimization/maximization, and
underestimation/overestimation. We study the four scenarios, and we 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 optimisation tasks
are concerned.
