Related papers: Havannah and TwixT are PSPACE-complete
In cooperative game theory, associated games allow for providing meaningful characterizations of solution concepts. Moreover, generalized values allow computing an influence or power index of each coalition in a game. In this paper, we view…
We study computational problems arising from the iterated removal of weakly dominated actions in anonymous games. Our main result shows that it is NP-complete to decide whether an anonymous game with three actions can be solved via iterated…
Fortification-interdiction games are tri-level adversarial games where two opponents act in succession to protect, disrupt and simply use an infrastructure for a specific purpose. Many such games have been formulated and tackled in the…
When solving k-in-a-Row games, the Hales-Jewett pairing strategy [4] is a well-known strategy to prove that specific positions are (at most) a draw. It requires two empty squares per possible winning line (group) to be marked, i.e., with a…
We study hedonic coalition formation games in which cooperation among the players is restricted by a graph structure: a subset of players can form a coalition if and only if they are connected in the given graph. We investigate the…
In this paper we study the fine-grained complexity of finding exact and approximate solutions to problems in P. Our main contribution is showing reductions from exact to approximate solution for a host of such problems. As one (notable)…
Several interconnection networks are based on the complete graph topology. Networks with a moderate size can be based on a single complete graph. However, large-scale networks such as Dragonfly and HyperX use, respectively, a hierarchical…
An alternating graph is a directed graph whose vertex set is partitioned into two classes, existential and universal. This forms the basic arena for a plethora of infinite duration two-player games where Player~$\square$ and~$\ocircle$…
We study the problem of conjunctive query evaluation relative to a class of queries; this problem is formulated here as the relational homomorphism problem relative to a class of structures A, wherein each instance must be a pair of…
The Sprague-Grundy (SG) theory reduces the sum of impartial games to the classical game of $NIM$. We generalize the concept of sum and introduce $\cH$-combinations of impartial games for any hypergraph $\cH$. In particular, we introduce the…
We study binary-action pairwise-separable network games that encompass both coordinating and anti-coordinating behaviors. Our model is grounded in an underlying directed signed graph, where each link is associated with a weight that…
We generalize the notion of convexity and average-convexity to the notion of weighted average-convexity. We show several results on the relation between weighted average-convexity and cooperative games. First, we prove that if a game is…
We analyze affine reachability problems in dimensions 1 and 2. We show that the reachability problem for 1-register machines over the integers with affine updates is PSPACE-hard, hence PSPACE-complete, strengthening a result by Finkel et…
We settle two long-standing complexity-theoretical questions-open since 1981 and 1993-in combinatorial game theory (CGT). We prove that the Grundy value (a.k.a. nim-value, or nimber) of Undirected Geography is PSPACE-complete to compute.…
Concurrent games with a fixed number of agents have been thoroughly studied, with various solution concepts and objectives for the agents. In this paper, we consider concurrent games with an arbitrary number of agents, and study the problem…
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:…
With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…
Finding the exact integrality gap $\alpha$ for the LP relaxation of the 2-edge-connected spanning multigraph problem (2EC) is closely related to the same problem for the Held-Karp relaxation of the metric traveling salesman problem (TSP).…
The notion of forbidden-transition graphs allows for a robust generalization of walks in graphs. In a forbidden-transition graph, every pair of edges incident to a common vertex is permitted or forbidden; a walk is compatible if all pairs…
We prove communication complexity lower bounds for (possibly mixed) Nash equilibrium in potential games. In particular, we show that finding a Nash equilibrium requires $poly(N)$ communication in two-player $N \times N$ potential games, and…