This paper considers a cognitive radio network in which each secondary user selects a primary user to assist in order to get a chance of accessing the primary user channel. Thus, each group of secondary users assisting the same primary user forms a coaltion. Within each coalition, sequential relaying is employed, and a relay ordering algorithm is used to make use of the relays in an efficient manner. It is required then to find the optimal sets of secondary users assisting each primary user such that the sum of their rates is maximized. The problem is formulated as a coalition formation game, and a Gibbs Sampling based algorithm is used to find the optimal coalition structure.
In this paper, we study the problem of cooperative interference management in an OFDMA two-tier small cell network. In particular, we propose a novel approach for allowing the small cells to cooperate, so as to optimize their sum-rate, while cooperatively satisfying their maximum transmit power constraints. Unlike existing work which assumes that only disjoint groups of cooperative small cells can emerge, we formulate the small cells' cooperation problem as a coalition formation game with overlapping coalitions. In this game, each small cell base station can choose to participate in one or mor…
Cooperation between rational users in wireless networks is studied using coalitional game theory. Using the rate achieved by a user as its utility, it is shown that the stable coalition structure, i.e., set of coalitions from which users have no incentives to defect, depends on the manner in which the rate gains are apportioned among the cooperating users. Specifically, the stability of the grand coalition (GC), i.e., the coalition of all users, is studied. Transmitter and receiver cooperation in an interference channel (IC) are studied as illustrative cooperative models to determine the stabl…
The paper uses a non-cooperative simultaneous game for coalition structure formation (Levando, 2016) to demonstrate some applications of the introduced game: a cooperation, a Bayesian game within a coalition with intra-coalition externalities, a stochastic game, where states are coalition structures; self-enforcement properties of a non-cooperative equilibrium and a construction of a non-cooperative stability criterion.
In wireless packet-forwarding networks with selfish nodes, application of a repeated game can induce the nodes to forward each others' packets, so that the network performance can be improved. However, the nodes on the boundary of such networks cannot benefit from this strategy, as the other nodes do not depend on them. This problem is sometimes known as {\em the curse of the boundary nodes}. To overcome this problem, an approach based on coalition games is proposed, in which the boundary nodes can use cooperative transmission to help the backbone nodes in the middle of the network. In return,…
We study coalition structure formation with intra and inter-coalition externalities in the introduced family of nested non-cooperative simultaneous finite games. A non-cooperative game embeds a coalition structure formation mechanism, and has two outcomes: an allocation of players over coalitions and a payoff for every player. Coalition structures of a game are described by Young diagrams. They serve to enumerate coalition structures and allocations of players over them. For every coalition structure a player has a set of finite strategies. A player chooses a coalition structure and a strategy…
Traditionally social sciences are interested in structuring people in multiple groups based on their individual preferences. This pa- per suggests an approach to this problem in the framework of a non- cooperative game theory. Definition of a suggested finite game includes a family of nested simultaneous non-cooperative finite games with intra- and inter-coalition externalities. In this family, games differ by the size of maximum coalition, partitions and by coalition structure formation rules. A result of every game consists of partition of players into coalitions and a payoff? profiles for e…
This paper introduces a novel approach that enables a number of cognitive radio devices that are observing the availability pattern of a number of primary users(PUs), to cooperate and use \emph{Bayesian nonparametric} techniques to estimate the distributions of the PUs' activity pattern, assumed to be completely unknown. In the proposed model, each cognitive node may have its own individual view on each PU's distribution, and, hence, seeks to find partners having a correlated perception. To address this problem, a coalitional game is formulated between the cognitive devices and an algorithm fo…
The paper defines a non-cooperative simultaneous finite game to study coalition structure formation with intra and inter-coalition externalities. The novelty of the game is that the game definition embeds a \textit{coalition structure formation mechanism}. This mechanism portions a set of strategies of the game into partition-specific strategy domains, what makes every partition to be a non-cooperative game with partition-specific payoffs for every player. The mechanism includes a maximum coalition size, a set of eligible partitions with coalitions sizes no greater than this number (which also…
Cooperative spectrum sensing has been shown to yield a significant performance improvement in cognitive radio networks. In this paper, we consider distributed cooperative sensing (DCS) in which secondary users (SUs) exchange data with one another instead of reporting to a common fusion center. In most existing DCS algorithms, the SUs are grouped into disjoint cooperative groups or coalitions, and within each coalition the local sensing data is exchanged. However, these schemes do not account for the possibility that an SU can be involved in multiple cooperative coalitions thus forming overlapp…
In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions--or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we int…
Cooperative transmission in vehicular networks is studied by using coalitional game and pricing in this paper. There are several vehicles and roadside units (RSUs) in the networks. Each vehicle has a desire to transmit with a certain probability, which represents its data burtiness. The RSUs can enhance the vehicles' transmissions by cooperatively relaying the vehicles' data. We consider two kinds of cooperations: cooperation among the vehicles and cooperation between the vehicle and RSU. First, vehicles cooperate to avoid interfering transmissions by scheduling the transmissions of the vehicl…
In this paper, the problem of random access contention between machine type devices (MTDs) in the uplink of a wireless cellular network is studied. In particular, the possibility of forming cooperative groups to coordinate the MTDs' requests for the random access channel (RACH) is analyzed. The problem is formulated as a stochastic coalition formation game in which the MTDs are the players that seek to form cooperative coalitions to optimize a utility function that captures each MTD's energy consumption and time-varying queue length. Within each coalition, an MTD acts as a coalition head that …
Collaborative Spectrum Sensing (CSS) between secondary users (SUs) in cognitive networks exhibits an inherent tradeoff between minimizing the probability of missing the detection of the primary user (PU) and maintaining a reasonable false alarm probability (e.g., for maintaining a good spectrum utilization). In this paper, we study the impact of this tradeoff on the network structure and the cooperative incentives of the SUs that seek to cooperate for improving their detection performance. We model the CSS problem as a non-transferable coalitional game, and we propose distributed algorithms fo…
Cooperative game theory deals with systems where players want to cooperate to improve their payoffs. But players may choose coalitions in a non-cooperative manner, leading to a coalition-formation game. We consider such a game with several players (willing to cooperate) and an adamant player (unwilling to cooperate) involved in resource-sharing. Here, the strategy of a player is the set of players with whom it wants to form a coalition. Given a strategy profile, an appropriate partition of coalitions is formed; players in each coalition maximize their collective utilities leading to a non-coop…
We study a cooperative game setting where the grand coalition may change since the initial players can invite more players. We focus on monotone games, i.e., adding more players to the grand coalition is not harmful. We model the invitation relationship as a directed acyclic graph. Our goal is to design a reward distribution mechanism for this new cooperative game setting such that players are incentivized to invite new players. In this paper, we propose the weighted permission Shapley value (inspired by permission structure and the weighted Shapley value) to achieve the goal. Our solution off…
Representation languages for coalitional games are a key research area in algorithmic game theory. There is an inherent tradeoff between how general a language is, allowing it to capture more elaborate games, and how hard it is computationally to optimize and solve such games. One prominent such language is the simple yet expressive Weighted Graph Games (WGGs) representation [14], which maintains knowledge about synergies between agents in the form of an edge weighted graph. We consider the problem of finding the optimal coalition structure in WGGs. The agents in such games are vertices in a g…
In many multiagent scenarios, agents distribute resources, such as time or energy, among several tasks. Having completed their tasks and generated profits, task payoffs must be divided among the agents in some reasonable manner. Cooperative games with overlapping coalitions (OCF games) are a recent framework proposed by Chalkiadakis et al. (2010), generalizing classic cooperative games to the case where agents may belong to more than one coalition. Having formed overlapping coalitions and divided profits, some agents may feel dissatisfied with their share of the profits, and would like to devi…
In wireless mesh network (WMN), multiple service providers (SPs) can cooperate to share resources (e.g., relay nodes and spectrum), to serve their collective subscribed customers for better service. As a reward, SPs are able to achieve more individual benefits, i.e., increased revenue or decreased cost, through efficient utilization of shared network resources. However, this cooperation can be realized only if fair allocation of aggregated payoff, which is the sum of the payoff of all the cooperative SPs, can be achieved. We first formulate such cooperation as a coalitional game with transfera…
We consider dynamic cooperative games, where the worth of coalitions varies over time according to the history of allocations. When defining the core of a dynamic game, we allow the possibility for coalitions to deviate at any time and thereby to give rise to a new environment. A coalition that considers a deviation needs to take the consequences into account because from the deviation point on, the game is no longer played with the original set of players. The deviating coalition becomes the new grand coalition which, in turn, induces a new dynamic game. The stage games of the new dynamical g…
Cooperative Game-Theoretic Credit Assignment for Multi-Agent Policy Gradients via the Core
Key Laboratory of Intelligence, Games and Information Processing in Shaanxi Province（陕西省智能信息处理重点实验室）；Unmanned System Research Institute（无人系统研究院）；Northwestern Polytechnical University（西北工业大学）；School of Mathematics and Statistics（数学与统计学院）；Information Science Academy（信息科学学院）；China Electronics Technology Group Corporation（中国电子科技集团有限公司）
Research in cooperative games often assumes that agents know the coalitional values with certainty, and that they can belong to one coalition only. By contrast, this work assumes that the value of a coalition is based on an underlying collaboration structure emerging due to existing but unknown relations among the agents; and that agents can form overlapping coalitions. Specifically, we first propose Relational Rules, a novel representation scheme for cooperative games with overlapping coalitions, which encodes the aforementioned relations, and which extends the well-known MC-nets representati…
Modern cellular networks are witnessing an unprecedented evolution from classical, centralized and homogenous architectures into a mix of various technologies, in which the network devices are densely and randomly deployed in a decentralized and heterogenous architecture. This shift in network architecture requires network devices to become more autonomous and, potentially, cooperate with one another. Such cooperation can, for example, take place between interfering small access points that seek to coordinate their radio resource allocation, nearby single-antenna users that can cooperatively p…
In this paper, a novel framework for normative modeling of the spectrum sensing and sharing problem in cognitive radios (CRs) as a transferable utility (TU) cooperative game is proposed. Secondary users (SUs) jointly sense the spectrum and cooperatively detect the primary user (PU) activity for identifying and accessing unoccupied spectrum bands. The games are designed to be balanced and super-additive so that resource allocation is possible and provides SUs with an incentive to cooperate and form the grand coalition. The characteristic function of the game is derived based on the worths of SU…
Cooperation between nodes sharing a wireless channel is becoming increasingly necessary to achieve performance goals in a wireless network. The problem of determining the feasibility and stability of cooperation between rational nodes in a wireless network is of great importance in understanding cooperative behavior. This paper addresses the stability of the grand coalition of transmitters signaling over a multiple access channel using the framework of cooperative game theory. The external interference experienced by each TX is represented accurately by modeling the cooperation game between th…
We analyze the core of a cooperative Cournot game. We assume that when contemplating a deviation, the members of a coalition assign positive probability over all possible coalition structures that the non-members can form. We show that when the number of firms in the market is sufficiently large then the core of the underlying cooperative game is non-empty. Moreover, we show that the core of our game is a subset of the γ- core.
I introduce cooperative product games (CPGs), a cooperative game where every player has a weight, and the value of a coalition is the product of the weights of the players in the coalition. I only look at games where the weights are at least $2$. I show that no player in such a game can be a dummy. I show that the game is convex, and therefore always has a non-empty core. I provide a simple method for finding a payoff vector in the core.
Coalition Formation Games for Distributed Cooperation Among Roadside Units in Vehicular Networks
UNIK - University Graduate Center, University of Oslo（奥斯陆大学研究生中心）；University of Houston（休斯顿大学）；Nanyang Technological University (NTU)（南洋理工大学）；University of Manitoba（曼尼托巴大学）
The computation of a solution concept of a cooperative game usually employs values of all coalitions. However, in some applications, the values of some of the coalitions might be unknown due to high costs associated with their determination or simply because it is not possible to determine them exactly. We introduce a method to approximate standard solution concepts based only on partial characteristic function of the cooperative game. In this paper, we build on our previous results and generalise the results of our methods to a significantly larger class of structures of incomplete informatio…
Exit-and-Join Dynamics and Equilibrium in Continuum Cooperative Games
Department of Electrical and Computer Engineering（电气与计算机工程系）；New York University Tandon School of Engineering（纽约大学塔恩工程学院）；Brooklyn, NY, USA（布鲁克林，纽约，美国）
With the rapid growth of sensor technology, smartphone sensing has become an effective approach to improve the quality of smartphone applications. However, due to time-varying wireless channels and lack of incentives for the users to participate, the quality and quantity of the data uploaded by the smartphone users are not always satisfying. In this paper, we consider a smartphone sensing system in which a platform publicizes multiple tasks, and the smartphone users choose a set of tasks to participate in. In the traditional non-cooperative approach with incentives, each smartphone user gets r…
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 lik…
We analyze cooperative Cournot games with boundedly rational firms. Due to cogni- tive constraints, the members of a coalition cannot accurately predict the coalitional structure of the non-members. Thus, they compute their value using simple heuris- tics. In particular, they assign various non-equilibrium probability distributions over the outsiders' set of partitions. We construct the characteristic function of a coalition in such an environment and we analyze the core of the corresponding games. We show that the core is non-empty provided the number of firms in the market is sufficiently la…
Cooperative interval game is a cooperative game in which every coalition gets assigned some closed real interval. This models uncertainty about how much the members of a coalition get for cooperating together. In this paper we study convexity, core and the Shapley value of games with interval uncertainty. Our motivation to do so is twofold. First, we want to capture which properties are preserved when we generalize concepts from classical cooperative game theory to interval games. Second, since these generalizations can be done in different ways, mainly with regard to the resulting level of un…
Cooperation between wireless network nodes is a promising technique for improving the physical layer security of wireless transmission, in terms of secrecy capacity, in the presence of multiple eavesdroppers. While existing physical layer security literature answered the question "what are the link-level secrecy capacity gains from cooperation?", this paper attempts to answer the question of "how to achieve those gains in a practical decentralized wireless network and in the presence of a secrecy capacity cost for information exchange?". For this purpose, we model the physical layer security c…
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 co…
In Cooperative Games with Externalities when the members of a set S \subset N of agents wish to deviate they need to calculate their worth. This worth depends on what the non-members (outsiders) N \setminus S will do, which in turn depends on which coalition structure the outsiders will form. Since this coalition formation problem is NP-hard, various approaches have been adopted. In this paper using an evolutionary game theoretic approach we provide a set of equations that can help agents in S reason about the coalition structures the outsiders may form in terms of minimum distances on an n-s …
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 coalition can guarantee itself, under any (including worst) conditions. We then investigate fundamental solution concepts of the considered cooperative game, namely the core and a variant of the min-max fair nucleolus. We consider two types of routing games based on the agents' Performance Objectives, namely bottleneck routing games and additive routing games…
Driven by both safety concerns and commercial interests, vehicular ad hoc networks (VANETs) have recently received considerable attentions. In this paper, we address popular content distribution (PCD) in VANETs, in which one large popular file is downloaded from a stationary roadside unit (RSU), by a group of on-board units (OBUs) driving through an area of interest (AoI) along a highway. Due to high speeds of vehicles and deep fadings of vehicle-to-roadside (V2R) channels, some of the vehicles may not finish downloading the entire file but only possess several pieces of it. To successfully se…
Microsoft Research（微软研究院）；Hebrew University（希伯来大学）
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 reliability extension, each agent only "survives" with a certain probability, and a coalition's value is the probability that its surviving members would be a winning coalition in the base game. We study prominent solution concepts in such games, showing how to approximate the Shapley value and how to compute the core in games with few agent types. We also show t…
The model of congestion games is widely used to analyze games related to traffic and communication. A central property of these games is that they are potential games and hence posses a pure Nash equilibrium. In reality it is often the case that some players cooperatively decide on their joint action in order to maximize the coalition's total utility. This is by modeled by Coalitional Congestion Games. Typical settings include truck drivers who work for the same shipping company, or routers that belong to the same ISP. The formation of coalitions will typically imply that the resulting coaliti…
Various peer-to-peer energy markets have emerged in recent years in an attempt to manage distributed energy resources in a more efficient way. One of the main challenges these models face is how to create and allocate incentives to participants. Cooperative game theory offers a methodology to financially reward prosumers based on their contributions made to the local energy coalition using the Shapley value, but its high computational complexity limits the size of the game. This paper explores a stratified sampling method proposed in existing literature for Shapley value estimation, and modifi…
In networked communications nodes choose among available actions and benefit from exchanging information through edges, while continuous technological progress fosters system functionings that increasingly often rely on cooperation. Growing attention is being placed on coalition formation, where each node chooses what coalition to join, while the surplus generated by cooperation is an amount of TU (transferable utility) quantified by a real-valued function defined on partitions -or even embedded coalitions- of nodes. A TU-sharing rule is thus essential, as how players are rewarded determines t…
Collaborative spectrum sensing among secondary users (SUs) in cognitive networks is shown to yield a significant performance improvement. However, there exists an inherent trade off between the gains in terms of probability of detection of the primary user (PU) and the costs in terms of false alarm probability. In this paper, we study the impact of this trade off on the topology and the dynamics of a network of SUs seeking to reduce the interference on the PU through collaborative sensing. Moreover, while existing literature mainly focused on centralized solutions for collaborative sensing, we…
We study a class of non-cooperative aggregative games -- denoted as \emph{social purpose games} -- in which the payoffs depend separately on a player's own strategy (individual benefits) and on a function of the strategy profile which is common to all players (social benefits) weighted by an individual benefit parameter. This structure allows for an asymmetric assessment of the social benefit across players. We show that these games have a potential and we investigate its properties. We investigate the payoff structure and the uniqueness of Nash equilibria and social optima. Furthermore, follo…
In cooperative games, the core is the most popular solution concept, and its properties are well known. In the classical setting of cooperative games, it is generally assumed that all coalitions can form, i.e., they are all feasible. In many situations, this assumption is too strong and one has to deal with some unfeasible coalitions. Defining a game on a subcollection of the power set of the set of players has many implications on the mathematical structure of the core, depending on the precise structure of the subcollection of feasible coalitions. Many authors have contributed to this topic,…
The concept of femtocell access points underlaying existing communication infrastructure has recently emerged as a key technology that can significantly improve the coverage and performance of next-generation wireless networks. In this paper, we propose a framework for macrocell-femtocell cooperation under a closed access policy, in which a femtocell user may act as a relay for macrocell users. In return, each cooperative macrocell user grants the femtocell user a fraction of its superframe. We formulate a coalitional game with macrocell and femtocell users being the players, which can take in…
