#### 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_{k}* (q) is within an absolute constant (depending only on k) of the sphere bound, 2^{q}/(_{≤k} ^{q}); 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

#### 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, 328-336. doi: 10.1016/j.jcta.2005.02.003

#### Publication Information

Journal of Combinatorial Theory. Series A