Related papers: Classic Nintendo Games are (Computationally) Hard
We analyze the computational complexity of several new variants of edge-matching puzzles. First we analyze inequality (instead of equality) constraints between adjacent tiles, proving the problem NP-complete for strict inequalities but…
Fire Emblem (FE) is a popular turn-based tactical role-playing game (TRPG) series on the Nintendo gaming consoles. This paper studies the computational complexity of a simplified version of FE (only floor tiles and wall tiles, the HP and…
Strong placement games (SP-games) are a class of combinatorial games whose structure allows one to describe the game via simplicial complexes. A natural question is whether well-known invariants of combinatorial games, such as "game value",…
Our ignorance of the winnability percentage of the solitaire card game `Klondike' has been described as ``one of the embarrassments of applied mathematics''. Klondike, the game in the Windows Solitaire program, is just one of many…
We prove that it is PPAD-hard to compute a Nash equilibrium in a tree polymatrix game with twenty actions per player. This is the first PPAD hardness result for a game with a constant number of actions per player where the interaction graph…
Cooperative games provide a framework to study cooperation among self-interested agents. They offer a number of solution concepts describing how the outcome of the cooperation should be shared among the players. Unfortunately, computational…
Parkinson's Disease (PD) is a progressive neurodegenerative movement disorder that affects more that 6 million people worldwide. Motor dysfunction gradually increases as the disease progress. It is usually mild in the early stages of the…
Serious games have proven to be effective tools for screening cognitive impairments and supporting diagnosis in patients with neurodegenerative diseases like Alzheimer's and Parkinson's. They also offer cognitive training benefits.…
Determining a Nash equilibrium in a $2$-player non-zero sum game is known to be PPAD-hard (Chen and Deng (2006), Chen, Deng and Teng (2009)). The problem, even when restricted to win-lose bimatrix games, remains PPAD-hard (Abbott, Kane and…
We prove that playing Candy Crush to achieve a given score in a fixed number of swaps is NP-hard.
In 2010, Bre\v{s}ar, Klav\v{z}ar and Rall introduced the optimization variant of the graph domination game and the game domination number, which was proved PSPACE-hard by Bre\v{s}ar et al. in 2016. In 2024, Leo Versteegen obtained the…
There has been a recent explosion in the capabilities of game-playing artificial intelligence. Many classes of RL tasks, from Atari games to motor control to board games, are now solvable by fairly generic algorithms, based on deep…
Feature-based SPL analysis and family-based model checking have seen rapid development. Many model checking problems can be reduced to two-player games on finite graphs. A prominent example is mu-calculus model checking, which is generally…
Classic Rock-Paper-Scissors, RPS, has seen many variants and generalizations in the past several years. In the previous paper, we defined playability and balance for games. We used these definitions to show that different forms of imbalance…
This paper investigates repeated win-lose coordination games (WLC-games). We analyse which protocols are optimal for these games, covering both the worst case and average case scenarios, i,e., optimizing the guaranteed and expected…
World-class human players have been outperformed in a number of complex two person games (Go, Chess, Checkers) by Deep Reinforcement Learning systems. However, owing to tractability considerations minimax regret of a learning system cannot…
Location-based games (LBG) impose virtual spaces on top of physical locations. Studies have explored LBG from various perspectives. However, a comprehensive study of who these players are, their traits, their gratifications, and the links…
We prove that Strings-and-Coins -- the combinatorial two-player game generalizing the dual of Dots-and-Boxes -- is strongly PSPACE-complete on multigraphs. This result improves the best previous result, NP-hardness, argued in Winning Ways.…
A simple game $(N,v)$ is given by a set $N$ of $n$ players and a partition of~$2^N$ into a set~$\mathcal{L}$ of losing coalitions~$L$ with value $v(L)=0$ that is closed under taking subsets and a set $\mathcal{W}$ of winning coalitions $W$…
Recent procedural content generation via machine learning (PCGML) methods allow learning from existing content to produce similar content automatically. While these approaches are able to generate content for different games (e.g. Super…