A Class of Sequential Games

Abstract

This paper considers a game between two players who choose from a collection of objects. The players make their choices alternately and Vi,j represents the value or amount that the ith player will gain if he selects the jth object. In relation to these values, the players may have various strategies or approaches to the game, and each of them constitutes a distinct theoretical problem. The paper formulates and solves three of these problems, each one having practical significance (for example, for the draft of professional football players).

How to Make the Most of a Shared Meal: Plan the Last Bite First

“…We thank the Centre for Experimental and Constructive Mathematics at Simon Fraser University for providing computer resources, and we are grateful to Elwyn Berlekamp, Kevin Doerksen, Eric LeGresley, James Propp, Scott Sheffield and Jonathan Wise for useful suggestions. Thanks to Renato Paes Leme for bringing reference [12] to our attention, and to anonymous referees whose astute suggestions significantly improved the paper.…”

“…We will give a new proof of the following theorem, which is due to Kohler and Chandrasekaran [12]. Theorem 1.…”

“…The subject of this paper is a strategy discovered by Kohler and Chandrasekaran [12], which we call the crossout strategy. Its mantra is:…”

“…. , n. Each dot in the figure represents the outcome of a strategy pair, with Alice's score plotted on the horizontal axis and Bob's score on the vertical axis, for the following permutation dinner of size 14: (2,14), (3,10), (4,3), (5,7), (6,5), (7,9), (8,8), (9,4), (10,13), (11,12), (12,11), (13,2), (14, 1)}.…”

Taking Turns

“…When a player does know the other's order and makes the appropriate use of it (as detailed below), we say he or she is being strategic. The optimality of the various strategic algorithms follows from special cases of a more general result of Kohler and Chandrasekaharan [4].…”