Related papers: Coalition Games on Interaction Graphs: A Horticult…
We consider the problem of determining the maximal $\alpha \in (0,1]$ such that every matching $M$ of size $k$ (or at most $k$) in a bipartite graph $G$ contains an induced matching of size at least $\alpha |M|$. This measure was recently…
We investigate whether explicit belief graphs improve LLM performance in cooperative multi-agent reasoning. Through 3,000+ controlled trials across four LLM families in the cooperative card game Hanabi, we establish four findings. First,…
The computation of a solution concept of a cooperative game usually employs values of all coalitions. However, in some applications, the values of some of the coalitions might be unknown due to high costs associated with their determination…
This paper proposes a novel algorithm to approximate the core of transferable utility (TU) cooperative games via linear programming. Given the computational hardness of determining the full core, our approach provides a tractable…
The core is a dominant solution concept in economics and cooperative game theory; it is predominantly used for profit, equivalently cost or utility, sharing. This paper demonstrates the versatility of this notion by proposing a completely…
We consider planning problems for graphs, Markov decision processes (MDPs), and games on graphs. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an…
We prove a theorem computing the number of solutions to a system of equations which is generic subject to the sparsity conditions embodied in a graph. We apply this theorem to games obeying graphical models and to extensive-form games. We…
Finding cohesive subgraphs in a network is a well-known problem in graph theory. Several alternative formulations of cohesive subgraph have been proposed, a notable example being $s$-club, which is a subgraph where each vertex is at…
Graph data has a unique structure that deviates from standard data assumptions, often necessitating modifications to existing methods or the development of new ones to ensure valid statistical analysis. In this paper, we explore the notion…
Admissibility has been studied for games of infinite duration with Boolean objectives. We extend here this study to games of infinite duration with quantitative objectives. First, we show that, un- der the assumption that optimal worst-case…
A matching game is a cooperative profit game defined on an edge-weighted graph, where the players are the vertices and the profit of a coalition is the maximum weight of matchings in the subgraph induced by the coalition. A population…
We investigate strong Nash equilibria in the \emph{max $k$-cut game}, where we are given an undirected edge-weighted graph together with a set $\{1,\ldots, k\}$ of $k$ colors. Nodes represent players and edges capture their mutual…
In Cooperative Games with Externalities when the members of a set S \subset N of agents wish to deviate they need to calculate their worth. This worth depends on what the non-members (outsiders) N \setminus S will do, which in turn depends…
A graph $G$ is a pairwise compatibility graph (PCG) if there exists an edge-weighted tree and an interval $I$, such that each leaf of the tree is a vertex of the graph, and there is an edge $\{ x, y \}$ in $G$ if and only if the weight of…
In evolutionary game theory, repeated two-player games are used to study strategy evolution in a population under natural selection. As the evolution greatly depends on the interaction structure, there has been growing interests in studying…
Many real-world systems are composed of interdependent networks that rely on one another. Such networks are typically designed and operated by different entities, who aim at maximizing their own payoffs. There exists a game among these…
Matchings and coverings are central topics in graph theory. The close relationship between these two has been key to many fundamental algorithmic and polyhedral results. For mixed graphs, the notion of matching forest was proposed as a…
We introduce a multi-modal autonomous delivery optimization framework as a coalition game for a fleet of UAVs and ADRs operating in two overlaying networks to address last-mile delivery in urban environments, including high-density areas…
Unlicensed secondary users (SUs) in cognitive radio networks are subject to an inherent tradeoff between spectrum sensing and spectrum access. Although each SU has an incentive to sense the primary user (PU) channels for locating spectrum…
We study potential games on unimodular random graphs of bounded degree, where players interact through the underlying network. Using the unimodular measure, we define a well-posed global potential that captures both finite- and…