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We introduce several methods of decomposition for two player normal form games. Viewing the set of all games as a vector space, we exhibit explicit orthonormal bases for the subspaces of potential games, zero-sum games, and their orthogonal…
Colonel Blotto games with discrete strategy spaces effectively illustrate the intricate nature of multidimensional strategic reasoning. This paper studies the equilibrium set of such games where, in line with prior experimental work, the…
The move-minimizing puzzles presented here are certain types of one-player combinatorial games that are shown to have explicit solutions whenever they can be encoded in a certain way as diamond-colored modular or distributive lattices. Our…
There have been recent efforts for incorporating Graph Neural Network models for learning full-stack solvers for constraint satisfaction problems (CSP) and particularly Boolean satisfiability (SAT). Despite the unique representational power…
The last decade has seen a revival of interest in pebble games in the context of proof complexity. Pebbling has proven a useful tool for studying resolution-based proof systems when comparing the strength of different subsystems, showing…
The cyclic sieving phenomenon (CSP) provides valuable data about symmetry classes of cyclic actions, and has applications to representation theory. In this paper, we enumerate domino tableaux of shape 2-by-n, and use this result to prove a…
Determinantal point processes (DPPs) are popular probabilistic models that arise in many machine learning tasks, where distributions of diverse sets are characterized by matrix determinants. In this paper, we develop fast algorithms to find…
Structural decomposition methods have been developed for identifying tractable classes of instances of fundamental problems in databases, such as conjunctive queries and query containment, of the constraint satisfaction problem in…
Although most reinforcement learning research has centered on competitive games, little work has been done on applying it to co-operative multiplayer games or text-based games. Codenames is a board game that involves both asymmetric…
This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, including examples like Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games,…
Multiplayer computer games play a big role in the ever-growing entertainment industry. Being competitive in this industry means releasing the best possible software, and reliability is a key feature to win the market. Computer games are…
Decision-making in large imperfect information games is difficult. Thanks to recent success in Poker, Counterfactual Regret Minimization (CFR) methods have been at the forefront of research in these games. However, most of the success in…
Two-player graph games have found numerous applications, most notably in the synthesis of reactive systems from temporal specifications, but also in verification. The relevance of infinite-state systems in these areas has lead to…
Games are often designed to shape player behavior in a desired way; however, it can be unclear how design decisions affect the space of behaviors in a game. Designers usually explore this space through human playtesting, which can be…
Evolutionary games on graphs play an important role in the study of evolution of cooperation in applied biology. Using rigorous mathematical concepts from a dynamical systems and graph theoretical point of view, we formalize the notions of…
The game of war is one of the most popular international children's card games. In the beginning of the game, the pack is split into two parts, then on each move the players reveal their top cards. The player having the highest card…
We introduce a variant of PCPs, that we refer to as rectangular PCPs, wherein proofs are thought of as square matrices, and the random coins used by the verifier can be partitioned into two disjoint sets, one determining the row of each…
This paper coins the notion of Joker games, a variant of concurrent games where the players are not strictly adversarial. Instead, Player 1 can get help from Player 2 by playing a Joker move. We formalize these games as cost games and…
We study an elementary two-player card game where in each round players compare cards and the holder of the smallest card wins. Using the rate equations approach, we treat the stochastic version of the game in which cards are drawn…
Japanese tatami mats are often arranged so that no four mats meet. This local restriction imposes a rich combinatorial structure when applied to monomino-domino coverings of rectilinear grids. We describe a modular, mechanical game board,…