Related papers: PSPACE-Hard 2D Super Mario Games: Thirteen Doors

We study routing games where every agent sequentially decides her next edge when she obtains the green light at each vertex. Because every edge only has capacity to let out one agent per round, an edge acts as a FIFO waiting queue that…

Game difficulty is a crucial aspect of game design, that can be directly influenced by tweaking game mechanics. Perceived difficulty can however also be influenced by simply altering the graphics to something more threatening. Here, we…

We investigate the complexity of finding a winning strategy for the mis\`ere version of three games played on graphs : two variants of the game $\text{NimG}$, introduced by Stockmann in 2004 and the game $\text{Vertex Geography}$ on both…

Human computation games (HCGs) can provide novel solutions to intractable computational problems, help enable scientific breakthroughs, and provide datasets for artificial intelligence. However, our knowledge about how to design and deploy…

In the famous Three-Door-Game Monte cannot help to win all the time by signaling location of the prize, using only the freedom he allowed to use. No matter which strategies played, there is always at least one door where the prize will not…

We prove PSPACE-completeness of Push-1: given a rectangular grid of 1 x 1 cells, each possibly occupied by a movable block, can a robot move from one specified location to another, given the ability to push up to one block at a time? In…

The Iterated Prisoner's Dilemma has guided research on social dilemmas for decades. However, it distinguishes between only two atomic actions: cooperate and defect. In real-world prisoner's dilemmas, these choices are temporally extended…

We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is…

Optimizing parameters of Two-Prover-One-Round Game (2P1R) is an important task in PCPs literature as it would imply a smaller PCP with the same or stronger soundness. While this is a basic question in PCPs community, the connection between…

The author has long enjoyed using the CSP refinement checker FDR to solve puzzles, as witnessed by examples in \cite{tpc,ucs}. Recent experiments have shown that a number of games of patience (card games for one) are now well within bounds.…

Noncooperative game theory provides a normative framework for analyzing strategic interactions. However, for the toolbox to be operational, the solutions it defines will have to be computed. In this paper, we provide a single reduction that…

In recent years, reinforcement learning has seen interest because of deep Q-Learning, where the model is a convolutional neural network. Deep Q-Learning has shown promising results in games such as Atari and AlphaGo. Instead of learning the…

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.…

We demonstrate that Col is PSPACE-complete on triangular grid graphs via a reduction from Bounded Two-Player Constraint Logic. This is the most structured graph family that Col is known to be computationally hard for.

Many problems in compositional synthesis and verification of multi-agent systems -- such as rational verification and assume-guarantee verification in probabilistic systems -- reduce to reasoning about two-player multi-objective stochastic…

We study linear constraint system (LCS) games over the ring of arithmetic modulo $d$. We give a new proof that certain LCS games (the Mermin--Peres Magic Square and Magic Pentagram over binary alphabets, together with parallel repetitions…

In the pinwheel problem, one is given an $m$-tuple of positive integers $(a_1, \ldots, a_m)$ and asked whether the integers can be partitioned into $m$ color classes $C_1,\ldots,C_m$ such that every interval of length $a_i$ has non-empty…

We establish the first hardness results for the problem of computing the value of one-round games played by a verifier and a team of provers who can share quantum entanglement. In particular, we show that it is NP-hard to approximate within…

Quoridor is an award-winning abstract strategy game designed by Mirko Marchesi and published in 1997. Similar games include Maze Attack, Blockade (also known as Cul-de-sac), and Pinko Pallino. In line with chess, checkers, Go, and other…

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",…