A liability allocation game

Article type: Research Article

Authors: Hankin, Robin K. S.

Affiliations: Auckland University of Technology, Auckland, New Zealand | Tel.: +64 9 9219999x5106; E-mail: robin.hankin@aut.ac.nz

Correspondence: [*] Corresponding author: Auckland University of Technology

Abstract: The following problem is considered. Two players are each required to allocate a quota of n counters among k boxes labelled 1, 2, … , k. At times t= 1, 2, 3, … a random box is identified; the probability of choosing box i is pi. If a player has at least one counter in the chosen box, she removes one counter from it; otherwise she takes no action. The winner is the first player to remove all her counters. The game so described may be modified so that each player simultaneously, but independently, identifies a box at random. This paper analyses this deceptively simple game, which has apparently not been studied in the literature. Some analytical and numerical results are then presented, followed by some challenges for further work.

Keywords: Zero-sum game, liability allocation game, allocation game, colonel Blotto, coupon collector’s problem

DOI: 10.3233/JCM-193658

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 20, no. 1, pp. 65-79, 2020