Definition:Quasi-Concave Total Preordering

Definition

Let $R^n$ be a real vector space.

Let $\precsim$ be a total preordering on $\R^n$.

Let $\precsim$ be such that:

for all $b \in \R^n$, the set $\left\{ {a \in \R^n: b \precsim a}\right\}$ is convex.

Then $\precsim$ is quasi-concave.

Also see

• Definition:Strictly Quasi-Concave Total Preordering

Sources

• 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): $1.7$: Terminology and Notation