On the Complexity of 2-Player Packing Games

TL;DR

This paper proves that determining the winner in two different 2-player packing games involving polycubes and a box is computationally PSPACE-complete, highlighting their inherent complexity.

Contribution

It establishes the PSPACE-completeness of outcome determination for two novel packing games, extending complexity results to these spatial combinatorial games.

Findings

Deciding game outcomes is PSPACE-complete.

Both games are computationally intractable under optimal play.

Results apply to games involving polycubes and spatial packing.

Abstract

We analyze the computational complexity of two 2-player games involving packing objects into a box. In the first game, players alternate drawing polycubes from a shared pile and placing them into an initially empty box in any available location; the first player who can't place another piece loses. In the second game, there is a fixed sequence of polycubes, and on a player's turn they drop the next piece in through the top of the box, after which it falls until it hits a previously placed piece (as in Tetris); the first player who can't place the next piece loses. We prove that in both games, deciding the outcome under perfect play is PSPACE-complete.