  Multiagent learning is a necessary yet challenging problem as multiagent
systems become more prevalent and environments become more dynamic. Much of the
groundbreaking work in this area draws on notable results from game theory, in
particular, the concept of Nash equilibria. Learners that directly learn an
equilibrium obviously rely on their existence. Learners that instead seek to
play optimally with respect to the other players also depend upon equilibria
since equilibria are fixed points for learning. From another perspective,
agents with limitations are real and common. These may be undesired physical
limitations as well as self-imposed rational limitations, such as abstraction
and approximation techniques, used to make learning tractable. This article
explores the interactions of these two important concepts: equilibria and
limitations in learning. We introduce the question of whether equilibria
continue to exist when agents have limitations. We look at the general effects
limitations can have on agent behavior, and define a natural extension of
equilibria that accounts for these limitations. Using this formalization, we
make three major contributions: (i) a counterexample for the general existence
of equilibria with limitations, (ii) sufficient conditions on limitations that
preserve their existence, (iii) three general classes of games and limitations
that satisfy these conditions. We then present empirical results from a
specific multiagent learning algorithm applied to a specific instance of
limited agents. These results demonstrate that learning with limitations is
feasible, when the conditions outlined by our theoretical analysis hold.
