Abstract
This paper provides an alternative approach to the existence of subgame-perfect equilibria with public randomization in continuous games of almost perfect information. Using the theory of weak integration, I study the topological properties of the continuation correspondences that describe the future evolution of play in any given stage of the game. This allows me to generalize to an infinite-dimensional setting the results of Simon and Zame [Simon, L.K., Zame, W.R., 1990. Discontinuous games and endogenous sharing rules. Econometrica 58, 861–872] on games with endogenous sharing rules. Thereby, I obtain a reformulation of the backward induction program for games of almost perfect information.
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