Related papers: Sprague-Grundy values and complexity for LCTR

Motivated by recent activity in low-dimensional topology, we provide a new criterion for left-orderability of a group under the assumption that the group is circularly-orderable: A group $G$ is left-orderable if and only if $G \times…

Efficient probabilistic inference by variable elimination in graphical models requires an optimal elimination order. However, finding an optimal order is a challenging combinatorial optimisation problem for models with a large number of…

We describe an efficient algorithm to compute solutions for the general two-player Blotto game on n battlefields with heterogeneous values. While explicit constructions for such solutions have been limited to specific, largely symmetric or…

Game-theoretic agents must make plans that optimally gather information about their opponents. These problems are modeled by partially observable stochastic games (POSGs), but planning in fully continuous POSGs is intractable without heavy…

Low-Rank Representation (LRR) is arguably one of the most powerful paradigms for Multi-view spectral clustering, which elegantly encodes the multi-view local graph/manifold structures into an intrinsic low-rank self-expressive data…

The satisfiability problem for branching-time temporal logics like CTL*, CTL and CTL+ has important applications in program specification and verification. Their computational complexities are known: CTL* and CTL+ are complete for doubly…

Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…

This paper is devoted to the study of closed string field theory in two dimensions. We compare two different approaches: BRST closed string field theory and the string effective Lagrangian. We show that the quadratic action and the pole…

We introduce the concept of budget games. Players choose a set of tasks and each task has a certain demand on every resource in the game. Each resource has a budget. If the budget is not enough to satisfy the sum of all demands, it has to…

Tree rotations (left and right) are basic local deformations allowing to transform between two unlabeled binary trees of the same size. Hence, there is a natural problem of practically finding such transformation path with low number of…

Parity games have witnessed several new quasi-polynomial algorithms since the breakthrough result of Calude et al. (STOC 2017). The combinatorial object underlying these approaches is a universal tree, as identified by Czerwi\'nski et al.…

Lagrangian descriptions of irreducible and reducible integer higher-spin representations of the Poincare group subject to a Young tableaux $Y[\hat{s}_1,\hat{s}_2]$ with two columns are constructed within a metric-like formulation in a…

Consider the following one-player game. Take a well-formed sequence of opening and closing brackets. As a move, the player can pair any opening bracket with any closing bracket to its right, erasing them. The goal is to re-pair (erase) the…

The connection between game theory, convex optimization, and geometry is deep. There are many applications of linear programming methods and polyhedral representation conversion methods in game theory. In this paper, we discuss two more…

Simulating bipartite games, such as the trust game, is not straightforward due to the lack of a natural way to distinguish roles in a single population. The square lattice topology can provide a simple yet elegant solution by alternating…

Reinforcement Learning (RL) has been able to solve hard problems such as playing Atari games or solving the game of Go, with a unified approach. Yet modern deep RL approaches are still not widely used in real-world applications. One reason…

In cooperative game theory, the primary focus is the equitable allocation of payoffs or costs among agents. However, in the practical applications of cooperative games, accurately representing games is challenging. In such cases, using an…

In the realm of artificial intelligence and card games, this study introduces a two-step reinforcement learning (RL) strategy tailored for "The Lord of the Rings: The Card Game (LOTRCG)," a complex multistage strategy card game. This…

We examine online safe multi-agent reinforcement learning using constrained Markov games in which agents compete by maximizing their expected total rewards under a constraint on expected total utilities. Our focus is confined to an episodic…

Open-world survival games pose significant challenges for AI algorithms due to their multi-tasking, deep exploration, and goal prioritization requirements. Despite reinforcement learning (RL) being popular for solving games, its high sample…