Equilibrium Identification Through the Lens of Constraint Set Engineering

Abstract Fixed-point theorems are fundamental in the decision sciences, but they fall short in models with multiple equilibria–especially in strategic market games –where existence results alone provide limited insight into the structure (trivial or otherwise) of the equilibrium set. This paper shows that, once equilibrium existence has been established, specific classes of equilibria can be characterised through an optimisation-based combination technique. The method is illustrated in a general, self-contained class of market games for which establishing equilibrium existence is itself nontrivial, and the identification of particular equilibrium types is considerably more demanding. A by-product of the analysis is an associated optimisation programme that is more tractable than the original equilibrium problem, especially with respect to second-order conditions. These conditions yield economically interpretable criteria for equilibrium selection. The proposed technique provides a tractable framework for theoretical and computational work in financial economics, management science, and applied econometrics, particularly in problems of parameter identification.