  A Fisher market is an economic model of buyer and seller interactions in
which each buyer's utility depends only on the bundle of goods she obtains.
Many people's interests, however, are affected by their social interactions
with others. In this paper, we introduce a generalization of Fisher markets,
namely influence Fisher markets, which captures the impact of social influence
on buyers' utilities. We show that competitive equilibria in influence Fisher
markets correspond to generalized Nash equilibria in an associated pseudo-game,
which implies the existence of competitive equilibria in all influence Fisher
markets with continuous and concave utility functions. We then construct a
monotone pseudo-game, whose variational equilibria and their duals together
characterize competitive equilibria in influence Fisher markets with
continuous, jointly concave, and homogeneous utility functions. This
observation implies that competitive equilibria in these markets can be
computed in polynomial time under standard smoothness assumptions on the
utility functions. The dual of this second pseudo-game enables us to interpret
the competitive equilibria of influence CCH Fisher markets as the solutions to
a system of simultaneous Stackelberg games. Finally, we derive a novel
first-order method that solves this Stackelberg system in polynomial time,
prove that it is equivalent to computing competitive equilibrium prices via
t\^{a}tonnement, and run experiments that confirm our theoretical results.
