Related papers: Multiple Hook Removing Game Whose Starting Positio…

The Unique Games Conjecture (UGC) constitutes a highly dynamic subarea within computational complexity theory, intricately linked to the outstanding P versus NP problem. Despite multiple insightful results in the past few years, a proof for…

In this note we prove the uniqueness of solutions to a class of Mean Field Games systems subject to possibly degenerate individual noise. Our results hold true for arbitrary long time horizons and for general non-separable Hamiltonians that…

In this paper, we study large population multi-agent reinforcement learning (RL) in the context of discrete-time linear-quadratic mean-field games (LQ-MFGs). Our setting differs from most existing work on RL for MFGs, in that we consider a…

This paper introduces a geometric framework for analyzing power relations in games, independent of their strategic form. We define a canonical preference space where each player's relational stance is a normalized vector. This model…

Reinforcement learning has increasingly been applied to economic decision-making, including taxation, public spending, and labor supply. However, existing RL-based economic models typically consider only a single government-household group,…

This paper develops a game-theoretic decision-making framework for autonomous driving in multi-agent scenarios. A novel hierarchical game-based decision framework is developed for the ego vehicle. This framework features an interaction…

Multiagent systems where agents interact among themselves and with a stochastic environment can be formalized as stochastic games. We study a subclass named Markov potential games (MPGs) that appear often in economic and engineering…

We consider the problem of simultaneous learning in stochastic games with many players in the finite-horizon setting. While the typical target solution for a stochastic game is a Nash equilibrium, this is intractable with many players. We…

Let $M^\sharp_n(\mathbb{R})$ denote the minimal active iterable extender model which has $n$ Woodin cardinals and contains all reals, if it exists, in which case we denote by $M_n(\mathbb{R})$ the class-sized model obtained by iterating the…

Domineering is a two-player game played on a checkerboard in which one player places dominoes vertically, while the other places them horizontally. In this paper, we find out the minimum number of moves for a game of Domineering to end on…

This letter presents an extended analysis and a novel upper bound of the subclass of Linear Quadratic Near Potential Differential Games (LQ NPDG). LQ NPDGs are a subclass of potential differential games, for which a distance between an LQ…

We study Nash equilibrium learning in partially observable Markov games (POMGs), a multi-agent reinforcement learning framework in which agents cannot fully observe the underlying state. Prior work in this setting relies on centralization…

A group of students in 7-9 grades are inventing combinatorial impartial games. The games are played on graphs, piles, and grids. We found winning positions, optimal strategies, and other interesting facts about the games.

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…

Simple Stochastic Games (SSGs) were introduced by Anne Condon in 1990, as the simplest version of Stochastic Games for which there is no known polynomial-time algorithm. Condon showed that Stochastic Games are polynomial-time reducible to…

Mean-payoff games play a central role in quantitative synthesis and verification. In a single-dimensional game a weight is assigned to every transition and the objective of the protagonist is to assure a non-negative limit-average weight.…

In this paper we study evolutive first order Mean Field Games in the Heisenberg group; each agent can move in the whole space but it has to follow "horizontal" trajectories which are given in terms of the vector fields generating the group…

We address in this paper Reinforcement Learning (RL) among agents that are grouped into teams such that there is cooperation within each team but general-sum (non-zero sum) competition across different teams. To develop an RL method that…

This thesis will be discussing scoring play combinatorial games and looking at the general structure of these games under different operators. I will also be looking at the Sprague-Grundy values for scoring play impartial games, and…

A large class of Positional Games are defined on the complete graph on $n$ vertices. The players, Maker and Breaker, take the edges of the graph in turns, and Maker wins iff his subgraph has a given -- usually monotone -- property. Here we…