The Complexity of Matching Games: A Survey

Matching games naturally generalize assignment games, a well-known class of cooperative games. Interest in matching games has grown recently due to some breakthrough results and new applications. This state-of-the-art survey provides an overview of matching games and extensions, such as $b$-matching games and partitioned matching games; the latter originating from the emerging area of international kidney exchange. In this survey we focus on computational complexity aspects of various game-theoretical solution concepts, such as the core, nucleolus and Shapley value, when the input is restricted to some (generalized) matching game

Complexity of Stability-based Solution Concepts in Multi-issue and MC-net Cooperative Games

ABSTRACT MC-nets constitute a natural compact representation scheme for cooperative games in multiagent systems. In this paper, we study the complexity of several natural computational problems that concern solution concepts such as the core, the least core and the nucleolus. We characterize the complexity of these problems for a variety of subclasses of MC-nets, also considering constraints on the game such as superadditivity (where appropriate). Many of our hardness results are derived from a hardness result that we establish for a class of multi-issue cooperative games (SILT games); we suspect that this hardness result can also be used to prove hardness for other representation schemes

Non-coherent successive relaying and cooperation: principles, designs, and applications

Cooperative communication is capable of forming a virtual antenna array for each node (user) in a network by allowing the nodes (users) to relay the messages of others to the destination. Such a relay aided network may be viewed as a distributed multiple-input multiple-output (MIMO) system relying on the spatially distributed single antennas of the cooperating mobiles, which avoids the correlation of the antenna elements routinely encountered in conventional MIMO systems and hence attains the maximum achievable diversity gain. Therefore, the family of cooperative communication techniques may be regarded as a potential solution for future wireless networks. However, constrained by the half-duplex transmit/receive mode of most practical transceivers, the cooperative networks may impose a severe 50% throughput loss. As a remedy, successive relaying can be employed, which is capable of mimicking a full-duplex relay and thereby recovering much of the 50% throughput loss. Furthermore, for the sake of bypassing power-hungry and potentially excessive-complexity channel estimation, noncoherent detection techniques may be employed for multiple-antenna aided systems, because estimating all the associated channels may become unrealistic. Explicitly, the mobile-stations acting as relays cannot be realistically expected to estimate the source-to-relay channels. In order to motivate further research on noncoherent successive relaying aided systems, a comprehensive review of its basic concepts, fundamental principles, practical transceiver designs and open challenges is provide

A Case for Cooperative Cloud Intermediaries for Small and Medium-Sized Enterprises

Cloud computing is a new and increasingly popular form of IT outsourcing. It implies that a cloud service provider offers very standardized abstract IT services which are accessed by a user over the Internet. While cloud services are supposed to be very beneficial for small and medium-sized enterprises, the adoption of such services has been low in this group, among other reasons because of high complexity of the cloud market and trust concerns. This paper motivates the notion of cooperative cloud intermediaries as a solution for these concerns by building on well-known concepts: transaction cost theory, agency theory, the notion of intermediaries in electronic markets and the cooperative paradigm. We derive our solution in detail and show its viability in theory

Cooperative Games with Bounded Dependency Degree

Cooperative games provide a framework to study cooperation among self-interested agents. They offer a number of solution concepts describing how the outcome of the cooperation should be shared among the players. Unfortunately, computational problems associated with many of these solution concepts tend to be intractable---NP-hard or worse. In this paper, we incorporate complexity measures recently proposed by Feige and Izsak (2013), called dependency degree and supermodular degree, into the complexity analysis of cooperative games. We show that many computational problems for cooperative games become tractable for games whose dependency degree or supermodular degree are bounded. In particular, we prove that simple games admit efficient algorithms for various solution concepts when the supermodular degree is small; further, we show that computing the Shapley value is always in FPT with respect to the dependency degree. Finally, we note that, while determining the dependency among players is computationally hard, there are efficient algorithms for special classes of games.Comment: 10 pages, full version of accepted AAAI-18 pape

Learning Cooperative Games

This paper explores a PAC (probably approximately correct) learning model in cooperative games. Specifically, we are given $m$ random samples of coalitions and their values, taken from some unknown cooperative game; can we predict the values of unseen coalitions? We study the PAC learnability of several well-known classes of cooperative games, such as network flow games, threshold task games, and induced subgraph games. We also establish a novel connection between PAC learnability and core stability: for games that are efficiently learnable, it is possible to find payoff divisions that are likely to be stable using a polynomial number of samples.Comment: accepted to IJCAI 201

Cooperation and Competition when Bidding for Complex Projects: Centralized and Decentralized Perspectives

To successfully complete a complex project, be it a construction of an airport or of a backbone IT system, agents (companies or individuals) must form a team having required competences and resources. A team can be formed either by the project issuer based on individual agents' offers (centralized formation); or by the agents themselves (decentralized formation) bidding for a project as a consortium---in that case many feasible teams compete for the contract. We investigate rational strategies of the agents (what salary should they ask? with whom should they team up?). We propose concepts to characterize the stability of the winning teams and study their computational complexity

Variance Allocation and Shapley Value

Motivated by the problem of utility allocation in a portfolio under a Markowitz mean-variance choice paradigm, we propose an allocation criterion for the variance of the sum of $n$ possibly dependent random variables. This criterion, the Shapley value, requires to translate the problem into a cooperative game. The Shapley value has nice properties, but, in general, is computationally demanding. The main result of this paper shows that in our particular case the Shapley value has a very simple form that can be easily computed. The same criterion is used also to allocate the standard deviation of the sum of $n$ random variables and a conjecture about the relation of the values in the two games is formulated.Comment: 20page

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