How to pick your football team

TL;DR

This paper analyzes a sequential team selection game with two captains dividing players with real-valued scores, proving that the starting captain cannot guarantee a win.

Contribution

It resolves a problem from 2015 by proving that the initial picker cannot ensure victory in this game.

Findings

Alice cannot guarantee a win regardless of strategy.

The game outcome depends on the players' scores and roles.

The result settles a question posed by Eccles in 2015.

Abstract

Team captains Alice and Bob divide up $2m$ footballers, each reduced to a real-valued score, into two teams of $m$ footballers each. On each turn, one captain plays picker, and the other chooser: the picker names a footballer yet to be selected, and the chooser decides which captain's team receives that footballer. Alice starts as picker, Bob as chooser, and roles alternate. The game ends as soon as either captain has a full team of $m$ footballers, at which point the other team receives all remaining footballers. The team with the larger sum of scores wins. Settling a problem raised by Eccles in 2015, we show that Alice cannot win.