Definition of a Downward Closed Feasible Set Single Parameter Environment (Game Theory)
Could someone give more clarification on what a downward closed feasible set?
So we have a Single Parameter Environment with feasible set X.
The definition given is: subsets of a feasible set are again feasible.
My first opinion of the definition seems to be that:
$X' subset X$ is a feasible set $forall X' subset X$.
However, this seems like a trivial observation.
Does downwardly closed mean that for any subset $X'$ of $X$, all $x' in X'$ are of form:
$$x' = {x_1, ldots, x_{i-1}, x_{i+1}, ldots, x_n}$$ and $${x_1, ldots, x_{i-1}, x_i, x_{i+1}, ldots, x_n} in X$$,
$X'$ is a feasible set.
optimization game-theory combinatorial-game-theory
asked Dec 1 at 2:13
Bojack Horseman
1117
add a comment |
Could someone give more clarification on what a downward closed feasible set?
So we have a Single Parameter Environment with feasible set X.
The definition given is: subsets of a feasible set are again feasible.
My first opinion of the definition seems to be that:
$X' subset X$ is a feasible set $forall X' subset X$.
However, this seems like a trivial observation.
Does downwardly closed mean that for any subset $X'$ of $X$, all $x' in X'$ are of form:
$$x' = {x_1, ldots, x_{i-1}, x_{i+1}, ldots, x_n}$$ and $${x_1, ldots, x_{i-1}, x_i, x_{i+1}, ldots, x_n} in X$$,
$X'$ is a feasible set.
optimization game-theory combinatorial-game-theory
asked Dec 1 at 2:13
Bojack Horseman
1117
add a comment |
Could someone give more clarification on what a downward closed feasible set?
So we have a Single Parameter Environment with feasible set X.
The definition given is: subsets of a feasible set are again feasible.
My first opinion of the definition seems to be that:
$X' subset X$ is a feasible set $forall X' subset X$.
However, this seems like a trivial observation.
Does downwardly closed mean that for any subset $X'$ of $X$, all $x' in X'$ are of form:
$$x' = {x_1, ldots, x_{i-1}, x_{i+1}, ldots, x_n}$$ and $${x_1, ldots, x_{i-1}, x_i, x_{i+1}, ldots, x_n} in X$$,
$X'$ is a feasible set.
optimization game-theory combinatorial-game-theory
asked Dec 1 at 2:13
Bojack Horseman
1117
Could someone give more clarification on what a downward closed feasible set?
So we have a Single Parameter Environment with feasible set X.
The definition given is: subsets of a feasible set are again feasible.
My first opinion of the definition seems to be that:
$X' subset X$ is a feasible set $forall X' subset X$.
However, this seems like a trivial observation.
Does downwardly closed mean that for any subset $X'$ of $X$, all $x' in X'$ are of form:
$$x' = {x_1, ldots, x_{i-1}, x_{i+1}, ldots, x_n}$$ and $${x_1, ldots, x_{i-1}, x_i, x_{i+1}, ldots, x_n} in X$$,
$X'$ is a feasible set.
optimization game-theory combinatorial-game-theory
optimization game-theory combinatorial-game-theory
asked Dec 1 at 2:13
Bojack Horseman
1117
asked Dec 1 at 2:13
Bojack Horseman
1117
asked Dec 1 at 2:13
Bojack Horseman
1117
asked Dec 1 at 2:13
Bojack Horseman
1117
asked Dec 1 at 2:13
Bojack Horseman
1117
1117
add a comment |
add a comment |
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