   Let $c,s,t$ be positive integers. We call an $s$-uniform a hypergraph an
$s$-graph. The $(c,s,t)$\emph{-Ramsey game} is played by Builder and Painter. Play
begins with an $s$-graph $G_{0}=(V,E_{0})$, where $E_{0}=\emptyset$ and $V$ is
determined by Builder. On the $i$th round Builder constructs a new edge $e_{i}$
and sets $G_{i}=(V,E_{i})$, where $E_{i}% =E_{i-1}\cup\{e_{i}\}$. Painter responds
by coloring $e_{i}$ with one of $c$ colors. Builder wins if Painter eventually
  creates a monochromatic copy of $K_{s}^{t}$, the complete $s$-graph on $t$
 vertices; otherwise Painter wins when she has colored all possible edges. We
extend the definition of coloring number to $s$-graphs in a natural way so that
 $\chi(G)\leq\operatorname*{col}(G)$ for any $s$-graph $G$ and then show that
Builder can win $(c,s,t)$-Ramsey game while building a hypergraph with coloring
number at most $\operatorname*{col}(K_{s}^{t})$. This relates to, but does not
answer, a question of Kurek, Ruci\'{n}ski and R\"{o}dl as to whether Builder can
win the $(2,2,t)$-Ramsey game while constructing an $s$-graph with substantially
  fewer than $\binom{\operatorname*{Ram}(t)}{2}$ edges. Our main tool is the
analysis of the following new game. Let $p$ be positive integers with $s\leq p$.
The $(p,s,t)$\emph{-survival game} is played by two players, \emph{Presenter} and
\emph{Chooser}. Play begins with the $s$-graph $H_{0}=(S_{0},E_{0})$ as in the
Ramsey game. At the beginning of the $i$th round the players will have constructed
an $s$-graph $H_{i-1}=(S_{i-1},E_{i-1})$. During the $i$th round they construct
 $H_{i}=(S_{i},E_{i})$ as follows. Presenter plays by presenting a $p$-subset
$P_{i}\subseteq S_{i-1}$. Chooser responds by choosing an $s$-set $X_{i}\subseteq
    P_{i}$. The remaining vertices in $P_{i}-X_{i}$ are discarded, leaving
$S_{i}=S_{i-1}-(P_{i}-X_{i})$ and \[ E_{i}=(E_{i-1}\cup\{X_{i}\})-\left\{ X_{j}\in
E_{i-1}:X_{j}\nsubseteq S_{i}\right\} . \] Presenter wins if $H_{i}$ contains the
   complete $s$-uniform hypergraph for some $i$; otherwise Chooser wins when
  $\left\vert S_{i}\right\vert <t$. \begin{theorem} \label{S}For all positive
   integers $p,s,t$ with $s\leq p$, Presenter has a winning strategy in the
$(p,s,t)$-survival game. \end{theorem} This is joint work with Goran Konjevod.