Equilibrium existence results for simple dynamic games

Abstract

The investigation of equilibrium existence in a salient class of multistage games is simplified and generalized by reducing them to singlestage games which correspond also to competitive economies. Thus, economic theory provides much of the motivation as well as method for the study. Working in locally convex topological vector spaces, a fixedpoint theorem of Fan is applied to show the existence of the Nash equilibria studied. En route, but also as a matter of interest in itself, certain topological foundations of the equilibrium analysis used are laid out. A particular feature of generality of the dynamic games studied is that the feasible control regions of individual players are allowed to depend on the past state-history and control-history. Another such feature is that the next-state map is allowed certain nonlinearities.