Related papers: On the Approximate Core and Nucleon of Flow Games …

We investigate a routing game that allows for the creation of coalitions, within the framework of cooperative game theory. Specifically, we describe the cost of each coalition as its maximin value. This represents the performance that the…

Cooperative games provide an appropriate framework for fair and stable profit distribution in multiagent systems. In this paper, we study the algorithmic issues on path cooperative games that arise from the situations where some commodity…

The computation of a solution concept of a cooperative game usually depends on values of all coalitions. However, in some applications, values of some of the coalitions might be unknown due to various reasons. We introduce a method to…

The nucleolus is a central solution concept in cooperative game theory. While its computation is NP-hard in general, it can be computed in polynomial time for convex games; however, the only published polynomial-time algorithm relies on the…

We study the approximate core for edge cover games, which are cooperative games stemming from edge cover problems. In these games, each player controls a vertex on a network $G = (V, E; w)$, and the cost of a coalition $S\subseteq V$ is…

We present a general framework to model strategic aspects and stable and fair resource allocations in networks via variants and generalizations of path coalitional games. In these games, a coalition of edges or vertices is successful if it…

The core is a central solution concept in cooperative game theory, defined as the set of feasible allocations or payments such that no subset of agents has incentive to break away and form their own subgroup or coalition. However, it has…

The arboricity of a graph is the minimum number of forests required to cover all its edges. In this paper, we examine arboricity from a game-theoretic perspective and investigate cost-sharing in the minimum forest cover problem. We…

Cooperative games provide a framework for fair and stable profit allocation in multi-agent systems. \emph{Core}, \emph{least-core} and \emph{nucleolus} are such solution concepts that characterize stability of cooperation. In this paper, we…

This paper defines a general class of cooperative games for which the nucleolus is efficiently computable. This class includes new members for which the complexity of computing their nucleolus was not previously known. We show that when the…

Policy makers focus on stable strategies as the ones adopted by rational players. If there are many such solutions an important question is how to select amongst them. We study this question for the Multicommodity Flow Coalition Game, used…

This paper addresses one of the most challenging issues in designing an efficient and sustainable ridesharing service: ridesharing market design. We formulate it as a fair cost allocation problem through the lens of the cooperative game…

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…

We introduce the novel notion of winning cores in parity games and develop a deterministic polynomial-time under-approximation algorithm for solving parity games based on winning core approximation. Underlying this algorithm are a number…

The classic paper of Shapley and Shubik \cite{Shapley1971assignment} characterized the core of the assignment game using ideas from matching theory and LP-duality theory and their highly non-trivial interplay. Whereas the core of this game…

We adopt a continuous-time dynamical system approach to study the evolution of the state of a game driven by the willingness to reduce the total dissatisfaction of the coalitions about their payment. Inspired by the work of Grabisch and…

The nucleolus offers a desirable payoff-sharing solution in cooperative games thanks to its attractive properties - it always exists and lies in the core (if the core is non-empty), and is unique. Although computing the nucleolus is very…

We fully characterize the core of a broad class of nonlinear games by identifying a suitable relaxation for inherent nonlinearity, directly generalizing the linear frameworks in the literature. This characterization significantly expands…

Nguyen and Thomas (2016) claimed that they have found a method to compute the nucleoli of games with more than $50$ players using nested linear programs (LP). Unfortunately, this claim is false. They incorrectly applied the indirect proof…

Motivated by civic problems such as participatory budgeting and multiwinner elections, we consider the problem of public good allocation: Given a set of indivisible projects (or candidates) of different sizes, and voters with different…