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We study a variant of online convex optimization where the player is permitted to switch decisions at most $S$ times in expectation throughout $T$ rounds. Similar problems have been addressed in prior work for the discrete decision set…
We introduce a quantitative framework for separating skill and chance in games by modeling them as complementary sources of control over stochastic decision trees. We define the Skill-Luck Index S(G) in [-1, 1] by decomposing game outcomes…
This paper focuses on procedurally generating rules and communicating them to players to adjust the difficulty. This is part of a larger project to collect and adapt games in educational games for young children using a digital puzzle game…
The combination of self-play and planning has achieved great successes in sequential games, for instance in Chess and Go. However, adapting algorithms such as AlphaZero to simultaneous games poses a new challenge. In these games, missing…
AlphaZero-style reinforcement learning (RL) algorithms have achieved superhuman performance in many complex board games such as Chess, Shogi, and Go. However, we showcase that these algorithms encounter significant and fundamental…
The classical Erdos-Szekeres theorem states that a convex $k$-gon exists in every sufficiently large point set. This problem has been well studied and finding tight asymptotic bounds is considered a challenging open problem. Several…
Red-blue pebble games model the computation cost of a two-level memory hierarchy. We present various hardness results in different red-blue pebbling variants, with a focus on the oneshot model. We first study the relationship between…
In this paper we present a novel genetic algorithm (GA) solution to a simple yet challenging commercial puzzle game known as the Zen Puzzle Garden (ZPG). We describe the game in detail, before presenting a suitable encoding scheme and…
Methods for dynamic difficulty adjustment allow games to be tailored to particular players to maximize their engagement. However, current methods often only modify a limited set of game features such as the difficulty of the opponents, or…
Hex is a turn-based two-player connection game with a high branching factor, making the game arbitrarily complex with increasing board sizes. As such, top-performing algorithms for playing Hex rely on accurate evaluation of board positions…
Crazyhouse is a chess variant that incorporates all of the classical chess rules, but allows users to drop pieces captured from the opponent as a normal move. Until 2018, all competitive computer engines for this board game made use of an…
Hedonic games provide a natural model of coalition formation among self-interested agents. The associated problem of finding stable outcomes in such games has been extensively studied. In this paper, we identify simple conditions on…
Games are a simplified model of reality and often serve as a favored platform for Artificial Intelligence (AI) research. Much of the research is concerned with game-playing agents and their decision making processes. The game of Guandan…
Since AlphaGo and AlphaGo Zero have achieved breakground successes in the game of Go, the programs have been generalized to solve other tasks. Subsequently, AlphaZero was developed to play Go, Chess and Shogi. In the literature, the…
The AlphaZero algorithm for the learning of strategy games via self-play, which has produced superhuman ability in the games of Go, chess, and shogi, uses a quantitative reward function for game outcomes, requiring the users of the…
The problem of matching markets has been studied for a long time in the literature due to its wide range of applications. Finding a stable matching is a common equilibrium objective in this problem. Since market participants are usually…
The mathematical structure of the widely popular Sudoku puzzles is akin to typical hard constraint satisfaction problems that lie at the heart of many applications, including protein folding and the general problem of finding the ground…
The block Lanczos algorithm proposed by Peter Montgomery is an efficient means to tackle the sparse linear algebra problem which arises in the context of the number field sieve factoring algorithm and its predecessors. We present here a…
We consider two-player games played in real time on game structures with clocks and parity objectives. The games are concurrent in that at each turn, both players independently propose a time delay and an action, and the action with the…
We investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NP-hard, while deciding whether a game has a…