Abstract
This paper considers the relation between complete inflation and perfect recall of information partitions in extensive games. It is proved that an information partition with perfect recall is completely inflated. This result, combined with Dalkey's theorem, shows that in the class of games (without chance moves) with perfect recall, a game is determinate if and only if every player has perfect information. A necessary and sufficient condition is provided for information partitions whose complete inflations have perfect recall.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Dalkey N (1953) Equivalence of information patterns and essentially determinate games. Annals of Math Studies 28, Princeton, pp 217–243
Kuhn HW (1953) Extensive games and the problem of information. Annals of Math Studies 28, Princeton, pp 193–216
Selten R (1975) Reexamination of the perfectness concept for equilibrium points in extensive games. Int J of Game Theory 4:25–55
Author information
Authors and Affiliations
Additional information
I would like to thank Professors Mitsuo Suzuki of Tokyo Institute of Technology and Mamoru Kaneko of Hitotsubashi University for their helpful discussions. I am also grateful to Johannes Heijmans for kindly showing me the proof of Lemma 5 which makes my earlier proof of Theorem 6 much shorter and clearer. All errors that remain are mine.
Rights and permissions
About this article
Cite this article
Okada, A. Complete inflation and perfect recall in extensive games. Int J Game Theory 16, 85–91 (1987). https://doi.org/10.1007/BF01780634
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01780634