  Systems of competing agents can often be modeled as games. Assuming
rationality, the most likely outcomes are given by an equilibrium (e.g. a Nash
equilibrium). In many practical settings, games are influenced by context, i.e.
additional data beyond the control of any agent (e.g. weather for traffic and
fiscal policy for market economies). Often the exact game mechanics are
unknown, yet vast amounts of historical data consisting of (context,
equilibrium) pairs are available, raising the possibility of learning a solver
which predicts the equilibria given only the context. We introduce Nash Fixed
Point Networks (N-FPNs), a class of neural networks that naturally output
equilibria. Crucially, N- FPNs employ a constraint decoupling scheme to handle
complicated agent action sets while avoiding expensive projections.
Empirically, we find N-FPNs are compatible with the recently developed
Jacobian-Free Backpropagation technique for training implicit networks, making
them significantly faster and easier to train than prior models. Our
experiments show N-FPNs are capable of scaling to problems orders of magnitude
larger than existing learned game solvers.
