  We introduce robust learning equilibrium. The idea of learning equilibrium is
that learning algorithms in multi-agent systems should themselves be in
equilibrium rather than only lead to equilibrium. That is, learning equilibrium
is immune to strategic deviations: Every agent is better off using its
prescribed learning algorithm, if all other agents follow their algorithms,
regardless of the unknown state of the environment. However, a learning
equilibrium may not be immune to non strategic mistakes. For example, if for a
certain period of time there is a failure in the monitoring devices (e.g., the
correct input does not reach the agents), then it may not be in equilibrium to
follow the algorithm after the devices are corrected. A robust learning
equilibrium is immune also to such non-strategic mistakes. The existence of
(robust) learning equilibrium is especially challenging when the monitoring
devices are 'weak'. That is, the information available to each agent at each
stage is limited. We initiate a study of robust learning equilibrium with
general monitoring structure and apply it to the context of auctions. We prove
the existence of robust learning equilibrium in repeated first-price auctions,
and discuss its properties.

Computer Science and Game Theory