  This paper takes a game theoretic approach to the design and analysis of
online algorithms and illustrates the approach on the finite-horizon ski-rental
problem. This approach allows beyond worst-case analysis of online algorithms.
First, we define "subgame optimality" which is stronger than worst case
optimality in that it requires the algorithm to take advantage of an adversary
not playing a worst case input. Algorithms only focusing on the worst case can
be far from subgame optimal. Second, we consider prior-independent design and
analysis of online algorithms, where rather than choosing a worst case input,
the adversary chooses a worst case independent and identical distribution over
inputs. Prior-independent online algorithms are generally analytically
intractable; instead we give a fully polynomial time approximation scheme to
compute them. Highlighting the potential improvement from these paradigms for
the finite-horizon ski-rental problem, we empirically compare worst-case,
subgame optimal, and prior-independent algorithms in the prior-independent
framework.
