Existence of subgame perfect equilibrium with public randomization: A short proof

Consider a multi−stage game where each player has a compact choice set and payoffs are continuous in all such choices. Harris, Reny and Robson (1995) prove existence of a subgame perfect equilibrium as long as a public correlation device is added to each stage. They achieve this by showing that the subgame perfect equilibium path correspondence is upper hemicontinuous. The present paper gives a short proof of existence that focuses on equilibrium payoffs rather than paths. We thank Chris Harris for helpful comments on this proof. Reny gratefully acknowledges support from the National Science Foundation (SES−9905599); Robson from the Social Sciences and Humanities Research Council of Canada. Citation: Reny, Philip J. and Arthur J. Robson, (2002) "Existence of subgame perfect equilibrium with public randomization: A short proof." Economics Bulletin, Vol. 3, No. 24 pp. 1−8 Submitted: October 4, 2002. Accepted: October 11, 2002. URL: http://www.economicsbulletin.com/2002/volume3/EB−02C70016A.pdf