Radzik (1991) showed that two-player games on compact intervals of the real line have " { equilibria for all " > 0, provided that payo® functions are upper semicontinuous and strongly quasi-concave. In an attempt to generalize this theorem, Ziad (1997) stated that the same is true for n-player games on compact, convex subsets of Rm, m ¸ 1 provided that we strengthen the upper semicontinuity condition. We show that: 1. the action spaces need to be polyhedral in order for Ziad's ap- proach to work, 2. Ziad's strong upper semicontinuity condition is equivalent to some form of quasi-polyhedral concavity of players' value func- tions in simple games, and 3. Radzik's Theorem is a corollary of (the corrected) Ziad's result.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Publisher Info
Paper provided by Universidade Nova de Lisboa, Faculdade de Economia in its series FEUNL Working Paper Series with number
wp488.
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.: