Extensive-form games and strategic complementarities

I prove the subgame-perfect equivalent of the basic result for Nash equilibria in normal-form games of strategic complements: the set of subgame-perfect equilibria is a non-empty, complete lattice. For this purpose I introduce a device that allows the study of the set of subgame-perfect equilibria as the set of fixed points of a correspondence. The correspondence has a natural interpretation. My results are limited because extensive-form games of strategic complementarities turn out— surprisingly—to be a very restrictive class of games. JEL Classification: C72, C73. ∗Department of Economics, University of California at Berkeley and Departamento de Economı́a, Facultad de Ciencias Sociales. email: [email protected]. I am very grateful to Ilya Segal and Chris Shannon for many helpful discussions. I also wish to thank Bob Anderson, and Matthew Rabin for their comments. The usual disclaimer applies.