Related papers: Projection onto the core: An optimal reallocation …
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…
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…
Concurrent multi-player mean-payoff games are important models for systems of agents with individual, non-dichotomous preferences. Whilst these games have been extensively studied in terms of their equilibria in non-cooperative settings,…
Cooperative games with nonempty core are called balanced, and the set of balanced games is a polyhedron. Given a game with empty core, we look for the closest balanced game, in the sense of the (weighted) Euclidean distance, i.e., the…
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…
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 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…
This paper studies many-to-one assignment markets, or matching markets with wages. Although it is well-known that the core of this model is non-empty, the structure of the core has not been fully investigated. To the known dissimilarities…
The core is a quintessential solution concept for profit sharing in cooperative game theory. An imputation allocates the worth of the given game among its agents. The imputation lies in the core of the game if, for each sub-coalition, the…
Reward allocation, also known as the credit assignment problem, has been an important topic in economics, engineering, and machine learning. An important concept in reward allocation is the core, which is the set of stable allocations where…
The matching game is a cooperative game where the value of every coalition is the maximum revenue of players in the coalition can make by forming pairwise disjoint partners. The multiple partners matching game generalizes the matching game…
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…
A solution concept on a class of transferable utility coalitional games is a multifunction satisfying given criteria of economic rationality. Every solution associates a set of payoff allocations with a coalitional game. This general…
Assignment games represent a tractable yet versatile model of two-sided markets with transfers. We study the likely properties of the core of randomly generated assignment games. If the joint productivities of every firm and worker are…
The space of finite games can be decomposed into three orthogonal subspaces [5], which are the subspaces of pure potential games, nonstrategic games and pure harmonic games. The orthogonal projections onto these subspaces are represented as…
The core of a game $v$ on $N$, which is the set of additive games $\phi$ dominating $v$ such that $\phi(N)=v(N)$, is a central notion in cooperative game theory, decision making and in combinatorics, where it is related to submodular…
LP-duality theory has played a central role in the study of cores of games, right from the early days of this notion to the present time. The classic paper of Shapley and Shubik \cite{Shapley1971assignment} introduced the "right" way of…
Game-theoretical approach to the analysis of parallel algorithms is proposed. The approach is based on presentation of the parallel computing as a congestion game. In the game processes compete for resources such as core of a central…
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 consider applications involving a large set of instances of projecting points to polytopes. We develop an intuition guided by theoretical and empirical analysis to show that when these instances follow certain structures, a large…