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Multiagent learning is a necessary yet challenging problem as multiagentsystems become more prevalent and environments become more dynamic. Much of thegroundbreaking work in this area draws on notable results from game theory, inparticular, the concept of Nash equilibria. Learners that directly learn anequilibrium obviously rely on their existence. Learners that instead seek toplay optimally with respect to the other players also depend upon equilibriasince equilibria are fixed points for learning. From another perspective,agents with limitations are real and common. These may be undesired physicallimitations as well as self-imposed rational limitations, such as abstractionand approximation techniques, used to make learning tractable. This articleexplores the interactions of these two important concepts: equilibria andlimitations in learning. We introduce the question of whether equilibriacontinue to exist when agents have limitations. We look at the general effectslimitations can have on agent behavior, and define a natural extension ofequilibria that accounts for these limitations. Using this formalization, wemake three major contributions: (i) a counterexample for the general existenceof equilibria with limitations, (ii) sufficient conditions on limitations thatpreserve their existence, (iii) three general classes of games and limitationsthat satisfy these conditions. We then present empirical results from aspecific multiagent learning algorithm applied to a specific instance oflimited agents. These results demonstrate that learning with limitations isfeasible, when the conditions outlined by our theoretical analysis hold.

Existence of Multiagent Equilibria with Limited Agents