Paul is trying to ascertain an unknown $x$, out of $n$ possibilities, from an adversary Carole by asking a series of $q$ queries.  In the standard ``Twenty Questions" Paul wins if and only if $n\leq 2^q$.

In Liar Games, Carole is allowed, under certain restrictions, to give an incorrect response, a lie.  She may do this at most $k$ times.  In this talk we examine asymptotics for $k$ fixed
and $q\rightarrow\infty$.
There is a natural connection between Liar Games and Coding Theory. The protocol must allow Paul to determine $x$ despite (at most) $k$ ``errors" in the ``transmission."  The major distinction is that
Paul's queries are sequential and can depend on previous responses.
We first discuss the ``classic" case where Carole has no further restrictions.
This game, often called the R\'enyi-Ulam game, has been very well studied.
Recent work has concentrated on the Half-Lie game.  Here, if the correct answer is yes then Carole {\em must} say yes.

In Coding Theory, this corresponds to the {\tt Z-}channel. (We shall further explore the game over other channels.) We show, basically,  that this increases the maximal $n$ for which Paul wins by a factor of $2^k$.

The techniques involve both linear algebra (creating a suitable weight function) and some interesting combinatorial notions on the Hamming cube.
Joint work with Ioana Dumitriu and Catherine Yan.