\begin{definition}[Definition:Conditional Preference]
Let $G$ be a lottery.
Let $P$ be a player of $G$.
Let $X$ denote the set of prizes which $P$ may receive.
Let $\Omega$ denote the set of possible states of $G$.
Let $\Xi$ be the event space of $G$.
Let $L$ be the set of all plays of $G$.
Let $f$ and $g$ be two lotteries in $G$.
Let $S \subseteq \Xi$ be an event.
A '''conditional preference''' is a preference relation $\succsim_S$ such that:
:$f \succsim_S g$ {{iff}} $f$ would be at least as desirable to $P$ as $g$, if $P$ was aware that the true state of the world was $S$.
That is, $f \succsim_S g$ {{iff}} $P$ prefers $f$ to $g$ and he knows only that $S$ has occurred.
The notation $a \sim_S b$ is defined as:
:$a \sim_S b$ {{iff}} $a \succsim_S b$ and $b \succsim_S a$
The notation $a \succ_S b$ is defined as:
:$a \succ_S b$ {{iff}} $a \succsim_S b$ and $a \not \sim_S a$
When no conditioning event $S$ is mentioned, the notation $a \succsim_\Omega b$, $a \succ_\Omega b$ and $a \sim_\Omega b$ can be used, which mean the same as $a \succsim b$, $a \succ b$ and $a \sim b$.
{{handwaving|Myerson is as lax as all the other game theory writers when it comes to defining rigorous concepts. I am going to have to abandon this field of study until I really understand exactly what the underlying mathematical objects are.}}
\end{definition}