The "Number Hides Game" on a Tree
A bachelor thesis in game theory
B.J.A. Swinkels (TU Delft - Electrical Engineering, Mathematics and Computer Science)
RJ Fokkink – Mentor (TU Delft - Applied Probability)
L.J.J. van Iersel – Graduation committee member (TU Delft - Discrete Mathematics and Optimization)
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Abstract
The "Number Hides Game" (NHG) is 2-player game played on a board that consists of a row of p consecutive coins. Player I and player II simultaneously choose subsets of m and n consecutive coins respectively. Player II pays the number of coins that lie in the intersection of the subsets to player I. This thesis introduces basic knowledge from the field of game theory needed to analyse the game. Afterwards, it presents and proves the optimal strategies of the NHG. Finally, a variant of the NHG will be discussed in which the board consist of a general tree instead of a row.