  In 1935, Erd\H{o}s and Szekeres proved that $(m-1)(k-1)+1$ is the minimum
number of points in the plane which definitely contain an increasing subset of
$m$ points or a decreasing subset of $k$ points (as ordered by their
$x$-coordinates). We consider their result from an on-line game perspective:
Let points be determined one by one by player A first determining the
$x$-coordinate and then player B determining the $y$-coordinate. What is the
minimum number of points such that player A can force an increasing subset of
$m$ points or a decreasing subset of $k$ points? We introduce this as the
Erd\H{o}s-Szekeres on-line number and denote it by $\text{ESO}(m,k)$. We
observe that $\text{ESO}(m,k) < (m-1)(k-1)+1$ for $m,k \ge 3$, provide a
general lower bound for $\text{ESO}(m,k)$, and determine $\text{ESO}(m,3)$ up
to an additive constant.
