“GAMES ON GRIDS, GRAPHS, AND HYPERGRAPHS” BY DARIN STEPHENSON, MATH/STATS DEPARTMENT

In this talk, we begin by considering a 2-player combinatorial game on an m by n grid. This game bears some
similarities to tic-tac-toe. The main difference is that this game can be played on any size grid (with potentially
some squares removed from play), and the game continues until the grid of playable squares is entirely full. The
game comes equipped with a scoring function by which the final positions of the two players can be evaluated. The
player who has amassed the most points wins. Our exploration of this game has involved two main threads:
developing theoretical results about the game and its optimal strategies, and training A.I. agents to play the game
well using reinforcement learning. 

While studying the grid game, we came across other work [Bagan, et. al. 2024] that defined a 2-player game that
can be played on any hypergraph. This game turned out to be a generalization of the game we had been studying on
grids. We will survey and extend some known results about this generalized hypergraph game. We will also give
details on some conjectures and open questions. As with the case of the grid game, we have developed some A.I.
agents that can learn to play the hypergraph game strategically.