Related papers: The General Graph Matching Game: Approximate Core
We give new characterizations of core imputations for the following games: * The assignment game. * Concurrent games, i.e., general graph matching games having non-empty core. * The unconstrained bipartite $b$-matching game (edges can be…
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…
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 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…
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…
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…
The assignment game is a classical model for profit sharing and a cornerstone of cooperative game theory. While an imputation in its core guarantees fairness among coalitions, it provides no fairness guarantee at the level of individual…
The assignment game, introduced by Shapley and Shubik (1971), is a classic model for two-sided matching markets between buyers and sellers. In the original assignment game, it is assumed that payments lead to transferable utility and that…
Cooperative games model the allocation of profit from joint actions, following considerations such as stability and fairness. We propose the reliability extension of such games, where agents may fail to participate in the game. In the…
LP-duality theory has played a central role in the study of the core, right from its early days to the present time. However, despite the extensive nature of this work, basic gaps still remain. We address these gaps using the following…
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…
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…
We study fair allocation of profit (or cost) for three central problems from combinatorial optimization: Max-Flow, MST and $b$-matching. The essentially unequivocal choice of solution concept for this purpose would be the core, because of…
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…
Coalition formation is a key problem in automated negotiation among self-interested agents, and other multiagent applications. A coalition of agents can sometimes accomplish things that the individual agents cannot, or can do things more…
In many multi-agent settings, participants can form teams to achieve collective outcomes that may far surpass their individual capabilities. Measuring the relative contributions of agents and allocating them shares of the reward that…
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,…
This paper concerns the analysis of the Shapley value in matching games. Matching games constitute a fundamental class of cooperative games which help understand and model auctions and assignments. In a matching game, the value of a…
In this dissertation, we analyze the computational properties of game-theoretic centrality measures. The key idea behind game-theoretic approach to network analysis is to treat nodes as players in a cooperative game, where the value of each…
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…