On General Minimax Theorems.¶
Sion, M. (1958). On General Minimax Theorems. Pacific Journal of Mathematics, 171-176.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Minimax Strategy
- The dual fact is the minimax inequality — max-min is at most min-max, with equality at a saddle point under specific convexity and compactness conditions — and the size of any gap measures how much the player forced to commit first loses to the player who responds optimally.
This sourceGeneralizes the minimax equality to quasi-concave-convex, semi-continuous functions, giving convexity/compactness-type conditions under which a saddle point exists (max-min = min-max).
Supported in partVerified against the work's full text
Sion's theorem gives equality of sup-inf and inf-sup for quasi-concave-convex, semicontinuous functions on compact convex sets; it does not discuss the inequality or the first-mover interpretation.
“Let M and N he convex, compact spaces, and f a function on MxN, quasi-concave-convex and u.s.c.-l.s.c”
- The dual fact is the minimax inequality — max-min is at most min-max, with equality at a saddle point under specific convexity and compactness conditions — and the size of any gap measures how much the player forced to commit first loses to the player who responds optimally.
Domain-specific¶
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 1 of 2 citations: 1 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:4d2a818e99ad · see in the full table