Related papers: Simplifying the Kohlberg Criterion on the Nucleolu…

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…

We provide an efficient algorithm for computing the nucleolus for an instance of a weighted cooperative matching game. This resolves a long-standing open question posed in [Faigle, Kern, Fekete, Hochst\"{a}ttler, Mathematical Programming,…

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…

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…

Minimal balanced collections are a generalization of partitions of a finite set of n elements and have important applications in cooperative game theory and discrete mathematics. However, their number is not known beyond n = 4. In this…

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…

We study bargaining games between suppliers and manufacturers in a network context. Agents wish to enter into contracts in order to generate surplus which then must be divided among the participants. Potential contracts and their surplus…

We extend the list of games where the nucleolus is computable in polynomial time. Based on the classical MPS scheme, nucleolus computation can be reduced to the problem of finding a coalition with minimum excess that does not belong to a…

Weighted voting games (WVG) are coalitional games in which an agent's contribution to a coalition is given by his it weight, and a coalition wins if its total weight meets or exceeds a given quota. These games model decision-making in…

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…

We consider cost allocation for set covering problems. We allocate as much cost to the elements (players) as possible without violating the group rationality condition (no subset of players pays more than covering this subset would cost),…

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…

We study the recently introduced fair division concept of the happy nucleolus for cost allocation among players in a cooperative game, with special focus on its computation. The happy nucleolus applies the same fairness criterion as the…

We study the nucleolus in a class of cooperative games where agents collaborate by sharing demands and production-distribution capacities across multiple markets. These production-distribution games form a structured subclass of linear…

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…

Coalitional games are mathematical models suited to analyze scenarios where players can collaborate by forming coalitions in order to obtain higher worths than by acting in isolation. A fundamental problem for coalitional games is to single…

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…

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…

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…