The Coefficient-Choosing Game
William Gasarch, Lawrence C. Washington, Sam Zbarsky

TL;DR
This paper investigates a strategic game involving two players choosing polynomial coefficients over an integral domain, analyzing which player has a winning strategy based on the properties of the domain.
Contribution
It characterizes the winning strategies for the game over various integral domains, extending understanding of polynomial roots and game theory in algebraic structures.
Findings
Identifies domains where Wanda has a winning strategy.
Determines conditions under which Nora can guarantee a win.
Provides a classification of domains based on the game's outcome.
Abstract
Let be an integral domain. Two players, Nora and Wanda, alternately choose coefficients from for a polynomial of degree . When they are done, if the polynomial has a root in the field of fractions of , then Wanda wins. If not, then Nora wins. We determine, for many , who wins this game.
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Taxonomy
Topicssemigroups and automata theory · Mathematical Dynamics and Fractals · Polynomial and algebraic computation
