Deciding the Winner of an Arbitrary Finite Poset Game is PSPACE-Complete

TL;DR

This paper proves that determining the winner of any finite poset game is PSPACE-complete, resolving previous uncertainty about its computational complexity and providing a reduction from Node Kayles.

Contribution

It establishes the PSPACE-completeness of arbitrary finite poset games through an explicit reduction from Node Kayles, a known PSPACE-complete problem.

Findings

Deciding the winner of a finite poset game is PSPACE-complete.

Polynomial algorithms exist for specific classes like Nim.

The paper provides a reduction from Node Kayles to poset games.

Abstract

A poset game is a two-player game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the poset loses. Polynomial time algorithms exist for certain restricted classes of poset games, such as the game of Nim. However, until recently the complexity of arbitrary finite poset games was only known to exist somewhere between NC^1 and PSPACE. We resolve this discrepancy by showing that deciding the winner of an arbitrary finite poset game is PSPACE-complete. To this end, we give an explicit reduction from Node Kayles, a PSPACE-complete game in which players vie to chose an independent set in a graph.