#### Document Type

Post-Print

#### Publication Date

11-2005

#### Abstract

The *q*-round Rényi-Ulam pathological liar game with *k* lies on the set [*n*] := {1,..., *n*} is a 2-player perfect information zero sum game. In each round Paul chooses a subset A ⊆ [*n*] and Carole either assigns 1 lie to each element of *A* or to each element of [*n*]\*A*. Paul wins if after *q* rounds there is at least one element with *k* or fewer lies. The game is dual to the original Rényi-Ulam liar game for which the winning condition is that at most one element has *k* or fewer lies. Define F** _{k}*(q) to be the minimum n such that Paul can win the q-round pathological liar game with k lies and initial set [n]. For fixed

*k*we prove that F*

*(q) is within an absolute constant (depending only on*

_{k}*k*) of the sphere bound, 2

^{q}/(

^{q}

_{≤k}); this is already known to hold for the original Rényi-Ulam liar game due to a result of J. Spencer.

#### Document Object Identifier (DOI)

10.1016/j.jcta.2005.02.003

#### Publisher

Elsevier

#### Repository Citation

Ellis, R.B., Ponomarenko, V., & Yan, C.H. (2005). The Rényi–Ulam pathological liar game with a fixed number of lies. *Journal of Combinatorial Theory. Series A, 112*(2), 328-336. doi:10.1016/j.jcta.2005.02.003

#### Publication Information

Journal of Combinatorial Theory. Series A