Approximations of solution concepts of cooperative games

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 approximate standard solution concepts based only on partial information given by a so called incomplete game. We demonstrate the ideas on the class of minimal incomplete games. Approximations are derived for different solution concepts including the Shapley value, the nucleolus, or the core. We show explicit formulas for approximations of some of the solution concepts and show how the approximability differs based on additional information about the game

Improving the Scalability of a Prosumer Cooperative Game with K-Means Clustering

Among the various market structures under peer-to-peer energy sharing, one model based on cooperative game theory provides clear incentives for prosumers to collaboratively schedule their energy resources. The computational complexity of this model, however, increases exponentially with the number of participants. To address this issue, this paper proposes the application of K-means clustering to the energy profiles following the grand coalition optimization. The cooperative model is run with the "clustered players" to compute their payoff allocations, which are then further distributed among the prosumers within each cluster. Case studies show that the proposed method can significantly improve the scalability of the cooperative scheme while maintaining a high level of financial incentives for the prosumers.Comment: 6 pages, 4 figures, 2 tables. Accepted to the 13th IEEE PES PowerTech Conference, 23-27 June 2019, Milano, Ital

An efficient algorithm for nucleolus and prekernel computation in some classes of TU-games

We consider classes of TU-games. We show that we can efficiently compute an allocation in the intersection of the prekernel and the least core of the game if we can efficiently compute the minimum excess for any given allocation. In the case where the prekernel of the game contains exactly one core vector, our algorithm computes the nucleolus of the game. This generalizes both a recent result by Kuipers on the computation of the nucleolus for convex games and a classical result by Megiddo on the nucleolus of standard tree games to classes of more general minimum cost spanning tree games. Our algorithm is based on the ellipsoid method and Maschler's scheme for approximating the prekernel. \u

Computing the Least-core and Nucleolus for Threshold Cardinality Matching Games

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 study the algorithmic issues on the least-core and nucleolus of threshold cardinality matching games (TCMG). A TCMG is defined on a graph $G=(V,E)$ and a threshold $T$, in which the player set is $V$ and the profit of a coalition $S\subseteq V$ is 1 if the size of a maximum matching in $G[S]$ meets or exceeds $T$, and 0 otherwise. We first show that for a TCMG, the problems of computing least-core value, finding and verifying least-core payoff are all polynomial time solvable. We also provide a general characterization of the least core for a large class of TCMG. Next, based on Gallai-Edmonds Decomposition in matching theory, we give a concise formulation of the nucleolus for a typical case of TCMG which the threshold $T$ equals $1$. When the threshold $T$ is relevant to the input size, we prove that the nucleolus can be obtained in polynomial time in bipartite graphs and graphs with a perfect matching

Strongly Essential Coalitions and the Nucleolus of Peer Group Games

Most of the known efficient algorithms designed to compute the nucleolus for special classes of balanced games are based on two facts: (i) in any balanced game, the coalitions which actually determine the nucleolus are essential; and (ii) all essential coalitions in any of the games in the class belong to a prespeci ed collection of size polynomial in the number of players.We consider a subclass of essential coalitions, called strongly essential coalitions, and show that in any game, the collection of strongly essential coalitions contains all the coalitions which actually determine the core, and in case the core is not empty, the nucleolus and the kernelcore.As an application, we consider peer group games, and show that they admit at most 2n - 1 strongly essential coalitions, whereas the number of essential coalitions could be as much as 2n-1. We propose an algorithm that computes the nucleolus of an n-player peer group game in O(n2) time directly from the data of the underlying peer group situation.game theory;algorithm;cooperative games;kernel estimation;peer games

The Least-core and Nucleolus of Path Cooperative Games

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 flows through a network. In these games, a coalition of edges or vertices is successful if it enables a path from the source to the sink in the network, and lose otherwise. Based on dual theory of linear programming and the relationship with flow games, we provide the characterizations on the CS-core, least-core and nucleolus of path cooperative games. Furthermore, we show that the least-core and nucleolus are polynomially solvable for path cooperative games defined on both directed and undirected network

Face to Face Negotiation to Overcome the Nimby Syndrome: Theory and Experimental Design

In recent decade, community after community has refused to accept facilities that require large amounts of land and generate local environmental costs such as airports, trash disposal plants or waste incinerators. Faced with this problem economists have used several methods such as lotteries, auctions or insurance policies. However, all those mechanisms have theoretical shortcomings. Therefore, we propose an approach based on face to face negotiation between elected representative. In order to reduce transaction costs, we introduce an arbitrator that proposes surplus distribution and a host community. The main question in this paper is to determine which distribution it has to propose to quickly reach an agreement. To answer this question we revise the traditional structure of cooperative games and explore the predictive power of three generalized solutions by implementing laboratory bargaining experiments Lors de la localisation d’équipements générateurs de nuisances tels que les décharges ou les incinérateurs, la commune d’accueil subit l’ensemble des coûts tandis que les autres communes perçoivent des bénéfices. Ainsi, fréquemment, les riverains du projet s’opposent à l’implantation et les projets de localisation n’aboutissent pas. Confrontés à ce problème, les économistes ont utilisés de nombreuses méthodes telles que les loteries, les enchères ou les assurances. Cependant, tous ces mécanismes ne parviennent pas à réduire l’opposition des riverains. Par conséquent, nous proposons une approche basée sur une négociation face à face entre les représentants des communes. Dans le but de réduire les coûts de transactions, nous introduisons un arbitre qui propose des répartitions de surplus et une commune d’accueil. La question principale dans cet article est de déterminer quelle répartition ce dernier doit proposer pour obtenir un accord rapidement. Pour répondre à cette question, nous révisons la structure traditionnelle des jeux coopératifs et testons le pouvoir prédictif de trois concepts de solution généralisés grâce à la réalisation d’expériences en laboratoirecooperative game theory, environmental economics, laboratory experiments, nimby syndrome, noxious facility siting, théorie des jeux coopératifs, économie de l’environnement, économie expérimentale, syndrome nimby, localisation d’équipements générateur de nuisances