Related papers: On the Complexity of Connection Games
We study three problems related to the computational complexity of the popular game Minesweeper. The first is consistency: given a set of clues, is there any arrangement of mines that satisfies it? This problem has been known to be…
We study algorithmic complexity of solving subtraction games in a~fixed dimension with a finite difference set. We prove that there exists a game in this class such that any algorithm solving the game runs in exponential time. Also we prove…
Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such…
Incomplete cooperative games generalise the classical model of cooperative games by omitting the values of some of the coalitions. This allows to incorporate uncertainty into the model and study the underlying games as well as possible…
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…
The $\mathscr{P}$-position sets of some combinatorial games have special combinatorial structures. For example, the $\mathscr{P}$-position set of the hexad game, first investigated by Conway and Ryba, is the block set of the Steiner system…
The game of SET is a popular card game in which the objective is to form Sets using cards from a special deck. In this paper we study single- and multi-round variations of this game from the computational complexity point of view and…
We revisit the complexity of the well-studied notion of Additively Separable Hedonic Games (ASHGs). Such games model a basic clustering or coalition formation scenario in which selfish agents are represented by the vertices of an…
Understanding the Impossibility of a Tie in Hex via Fixed Point Theorems, the Hex Theorem, and Their Equivalence.
We show that the widely used homotopy method for solving fixpoint problems, as well as the Harsanyi-Selten equilibrium selection process for games, are PSPACE-complete to implement. Extending our result for the Harsanyi-Selten process, we…
Temporal graphs extend ordinary graphs with discrete time that affects the availability of edges. We consider solving games played on temporal graphs where one player aims to explore the graph, i.e., visit all vertices. The complexity…
In this paper, we resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPAD-complete, along with the domains of practical significance:…
We put forward a new model of congestion games where agents have uncertainty over the routes used by other agents. We take a non-probabilistic approach, assuming that each agent knows that the number of agents using an edge is within a…
A semilinear relation S is max-closed if it is preserved by taking the componentwise maximum. The constraint satisfaction problem for max-closed semilinear constraints is at least as hard as determining the winner in Mean Payoff Games, a…
We investigate the difficulty of finding economically efficient solutions to coordination problems on graphs. Our work focuses on two forms of coordination problem: pure-coordination games and anti-coordination games. We consider three…
We study the following combinatorial game played by two players, Alice and Bob, which generalizes the Pizza game considered by Brown, Winkler and others. Given a connected graph G with nonnegative weights assigned to its vertices, the…
We analyze some of the many game mechanics available to Link in the classic Legend of Zelda series of video games. In each case, we prove that the generalized game with that mechanic is polynomial, NP-complete, NP-hard and in PSPACE, or…
Adversarial training, a special case of multi-objective optimization, is an increasingly prevalent machine learning technique: some of its most notable applications include GAN-based generative modeling and self-play techniques in…
Temporal graphs are a popular modelling mechanism for dynamic complex systems that extend ordinary graphs with discrete time. Simply put, time progresses one unit per step and the availability of edges can change with time. We consider the…
The additively separable hedonic game (ASHG) is a model of coalition formation games on graphs. In this paper, we intensively and extensively investigate the computational complexity of finding several desirable solutions, such as a Nash…