We show that there is a broad range of systems of simultaneous equations that arise in economics as descriptions of equilibrium that can be solved in elementary fashion via degree theory. Some of these systems are not susceptible to analysis by standard Brouwer ﬁxed point methods. Two of our applications are to general equilibrium with incomplete markets, and to nonconvex production with noncompetitive pricing rules.
Geanakoplos, John and Shafer, Wayne, "Solving Systems of Simultaneous Equations in Economics" (1989). Cowles Foundation Discussion Papers. 1146.