  Time-inconsistency is a characteristic of human behavior in which people plan
for long-term benefits but take actions that differ from the plan due to
conflicts with short-term benefits. Such time-inconsistent behavior is believed
to be caused by present bias, a tendency to overestimate immediate rewards and
underestimate future rewards. It is essential in behavioral economics to
investigate the relationship between present bias and time-inconsistency. In
this paper, we propose a model for analyzing agent behavior with present bias
in tasks to make progress toward a goal over a specific period. Unlike previous
models, the state sequence of the agent can be described analytically in our
model. Based on this property, we analyze three crucial problems related to
agents under present bias: task abandonment, optimal goal setting, and optimal
reward scheduling. Extensive analysis reveals how present bias affects the
condition under which task abandonment occurs and optimal intervention
strategies. Our findings are meaningful for preventing task abandonment and
intervening through incentives in the real world.
