Searching Games: A Bound for the Responder

A searching game with two unknowns and a lie involves two players, the responder and the questioner. Before the start of the game, the two parties predetermine an amount of numbers n to consider, and how many questions k the questioner can ask before the game ends with a victory (or loss) for the responder. The responder thinks of two secret numbers. The questioner asks questions of the form How many of your two numbers are in the subset Q of the set {0,...,n-1}? , in an attempt to search and find what the two secret numbers are. If the questioner identifies the two secret numbers within the agreed upon number of questions k, the questioner wins. The responder is allowed to lie in the game at most one time. We identify a bound on n and k for which the responder is guaranteed to win.This research was completed as part of an Alayont Fellowship in the Fall of 2019