We analyse a coalition formation game between strategic service providers of a congestible service. The key novelty of our formulation is that it is a constant sum game, i.e., the total payoff across all service providers (or coalitions of providers) is fixed, and dictated by the total size of the market. The game thus captures the tension between resource pooling (to benefit from the resulting statistical economies of scale) and competition between coalitions over market share. In a departure from the prior literature on resource pooling for congestible services, we show that the grand coalition is in general not stable, once we allow for competition over market share. Instead, the stable configurations are duopolies, where the dominant coalition exploits its economies of scale to corner a disproportionate market share. We analyse the stable duopolies that emerge from this interaction, and also study a dynamic variant of this game.
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.
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…
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…
This work shows that the formation of a finite number of coalitions in a nonatomic network congestion game benefits everyone. At the equilibrium of the composite game played by coalitions and individuals, the average cost to each coalition and the individuals' common cost are all lower than in the corresponding nonatomic game (without coalitions). The individuals' cost is lower than the average cost to any coalition. Similarly, the average cost to a coalition is lower than that to any larger coalition. Whenever some members of a coalition become individuals, the individuals' payoff is increase…
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…
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…
In this paper, we consider the consistency of the desirability relation with the ranking of the players in a simple game provided by some well-known solutions, in particular the Public Good Index [14] and the criticality-based ranking [1]. We define a new ranking solution, the Lexicographic Ranking based on Minimal winning coalitions (LRM), strongly related to the Public Good Index being rooted in the minimal winning coalitions of the simple game, proving that it is monotonic with respect to the desirability relation [17], when it holds. A suitable characterization of the LRM solution is provi…
Nguyen et al. [1] introduced altruistic hedonic games in which agents' utilities depend not only on their own preferences but also on those of their friends in the same coalition. We propose to extend their model to coalition formation games in general, considering also the friends in other coalitions. Comparing our model to altruistic hedonic games, we argue that excluding some friends from the altruistic behavior of an agent is a major disadvantage that comes with the restriction to hedonic games. After introducing our model and showing some desirable properties, we additionally study some c…
This paper studies a significant problem in green networking called switching off base stations in case of cooperating service providers by means of stochastic geometric and coalitional game tools. The coalitional game herein considered is played by service providers who cooperate in switching off base stations. When they cooperate, any mobile is associated to the nearest BS of any service provider. Given a Poisson point process deployment model of nodes over an area and switching off base stations with some probability, it is proved that the distribution of signal to interference plus noise r…
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…
Mobile edge computing (MEC), affords service to the vicinity of mobile devices (MDs), has become a key technology for future network. Offloading big data to the MEC server for preprocessing is a attractive choice of MDs. In the paper, we investigate data offloading from MDs to MEC servers. A coalitional game based pricing scheme is proposed. We apply coalitional game to depict the offloading relationship between MDs and MEC servers, and utilize pricing as the stimuli for the offloading. A scheduled MD chooses one MEC server within the same coalition for offloading, and pays the selected MEC se…
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…
In this paper, we examine \emph{hedonic coalition formation games} in which each player's preferences over partitions of players depend only on the members of his coalition. We present three main results in which restrictions on the preferences of the players guarantee the existence of stable partitions for various notions of stability. The preference restrictions pertain to \emph{top responsiveness} and \emph{bottom responsiveness} which model optimistic and pessimistic behavior of players respectively. The existence results apply to natural subclasses of \emph{additive separable hedonic game…
This paper studies the Nash stability in hedonic coalition formation games. We address the following issue: for a general problem formulation, is there any utility allocation method ensuring a Nash-stable partition? We propose the definition of the Nash-stable core. We study the conditions for having a non-empty Nash-stable core. More precisely, we show how relaxed efficiency in utility sharing method allows to ensure a non-empty Nash-stable core.
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…
Hedonic games formalize coalition formation scenarios where players evaluate an outcome based on the coalition they are contained in. Due to a large number of possible coalitions, compact representations of these games are crucial. We complement known compact representation models by a distance-based approach: Players' preferences are encoded in a bipolar manner by ordinal preferences over a small set of known neighbouring players, coalitions are represented by adequate preference orders from a player's perspective, and preferences over coalitions are extended based on a directed form of Hausd…
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…
We revisit the coalition structure generation problem in which the goal is to partition the players into exhaustive and disjoint coalitions so as to maximize the social welfare. One of our key results is a general polynomial-time algorithm to solve the problem for all coalitional games provided that player types are known and the number of player types is bounded by a constant. As a corollary, we obtain a polynomial-time algorithm to compute an optimal partition for weighted voting games with a constant number of weight values and for coalitional skill games with a constant number of skills. W…
The article introduces a notion of a stochastic game with failure states and proposes two logical systems with modality "coalition has a strategy to transition to a non-failure state with a given probability while achieving a given goal." The logical properties of this modality depend on whether the modal language allows the empty coalition. The main technical results are a completeness theorem for a logical system with the empty coalition, a strong completeness theorem for the logical system without the empty coalition, and an incompleteness theorem which shows that there is no strongly compl…
We propose a notion of a stable partition in a coalitional game that is parametrized by the concept of a defection function. This function assigns to each partition of the grand coalition a set of different coalition arrangements for a group of defecting players. The alternatives are compared using their social welfare. We characterize the stability of a partition for a number of most natural defection functions and investigate whether and how so defined stable partitions can be reached from any initial partition by means of simple transformations. The approach is illustrated by analyzing an e…
We propose an abstract approach to coalition formation that focuses on simple merge and split rules transforming partitions of a group of players. We identify conditions under which every iteration of these rules yields a unique partition. The main conceptual tool is a specific notion of a stable partition. The results are parametrized by a preference relation between partitions of a group of players and naturally apply to coalitional TU-games, hedonic games and exchange economy games.
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 …
NICTA（澳大利亚国家信息与通信技术研究院）；University of New South Wales（新南威尔士大学）；University of Oxford（牛津大学）；Université Paris-Dauphine（巴黎第九大学）
We study hedonic games with dichotomous preferences. Hedonic games are cooperative games in which players desire to form coalitions, but only care about the makeup of the coalitions of which they are members; they are indifferent about the makeup of other coalitions. The assumption of dichotomous preferences means that, additionally, each player's preference relation partitions the set of coalitions of which that player is a member into just two equivalence classes: satisfactory and unsatisfactory. A player is indifferent between satisfactory coalitions, and is indifferent between unsatisfacto…
A matching game is a cooperative profit game defined on an edge-weighted graph, where the players are the vertices and the profit of a coalition is the maximum weight of matchings in the subgraph induced by the coalition. A population monotonic allocation scheme is a collection of rules defining how to share the profit among players in each coalition such that every player is better off when the coalition expands. In this paper, we study matching games and provide a necessary and sufficient characterization for the existence of population monotonic allocation schemes. Our characterization also…
We consider coalition formation games in which each player has preferences over the other players and his preferences over coalitions are based on the best player ($\mathcal{B}$-/B-hedonic games) or the worst player ($\mathcal{W}$/W-hedonic games) in the coalition. We show that for $\mathcal{B}$-hedonic games, an individually stable partition is guaranteed to exist and can be computed efficiently. Similarly, there exists a polynomial-time algorithm which returns a Nash stable partition (if one exists) for $\mathcal{B}$-hedonic games with strict preferences. Both $\mathcal{W}$- and W-hedonic ga…
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 coalition formation games self-organized coalitions are created as a result of the strategic interactions of independent agents. For each couple of agents $(i,j)$, weight $w_{i,j}=w_{j,i}$ reflects how much agents $i$ and $j$ benefit from belonging to the same coalition. We consider the modified fractional hedonic game, that is a coalition formation game in which agents' utilities are such that the total benefit of agent $i$ belonging to a coalition (given by the sum of $w_{i,j}$ over all other agents $j$ belonging to the same coalition) is averaged over all the other members of that coalit…
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…
We study the computational complexity of finding stable outcomes in hedonic games, which are a class of coalition formation games. We restrict our attention to symmetric additively-separable hedonic games, which are a nontrivial subclass of such games that are guaranteed to possess stable outcomes. These games are specified by an undirected edge- weighted graph: nodes are players, an outcome of the game is a partition of the nodes into coalitions, and the utility of a node is the sum of incident edge weights in the same coalition. We consider several stability requirements defined in the liter…
This paper considers the problem of dividing agents among coalitions. We concentrate on Additively Separable Hedonic Games (ASHG's), in which each agent has a non-negative value for every other agent and her utility is the sum of the values she assigns to the members of her coalition. Unlike previous work, we analyze a model where exactly $k$ coalitions must be formed, and the goal is to maximize the utility of the agent which is worst off, i.e., the egalitarian social welfare. We show that this problem is hard, even when the number of agents should be equally divided among the coalitions. We …
Microsoft Research（微软研究院）；University of Southampton（南安普顿大学）；Nanyang Technological University（南洋理工大学）；Hebrew University（希伯来大学）；Heinrich-Heine-Universität Düsseldorf（杜塞尔多夫海因里希·海涅大学）
A key question in cooperative game theory is that of coalitional stability, usually captured by the notion of the \emph{core}--the set of outcomes such that no subgroup of players has an incentive to deviate. However, some coalitional games have empty cores, and any outcome in such a game is unstable. In this paper, we investigate the possibility of stabilizing a coalitional game by using external payments. We consider a scenario where an external party, which is interested in having the players work together, offers a supplemental payment to the grand coalition (or, more generally, a particul…
Coalitional voting games appear in different forms in multi-agent systems, social choice and threshold logic. In this paper, the complexity of comparison of influence between players in coalitional voting games is characterized. The possible representations of simple games considered are simple games represented by winning coalitions, minimal winning coalitions, weighted voting game or a multiple weighted voting game. The influence of players is gauged from the viewpoint of basic player types, desirability relations and classical power indices such as Shapley-Shubik index, Banzhaf index, Holle…
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…
In hedonic games, players form coalitions based on individual preferences over the group of players they could belong to. Several concepts to describe the stability of coalition structures in a game have been proposed and analysed in the literature. However, prior research focuses on algorithms with time complexity that is at least linear in the input size. In the light of very large games that arise from, e.g., social networks and advertising, we initiate the study of sublinear time property testing algorithms for existence and verification problems under several notions of coalition stabilit…
We examine cooperative games where the viability of a coalition is determined by whether or not its members have the ability to communicate amongst themselves independently of non-members. This necessary condition for viability was proposed by Myerson (1977) and is modeled via an interaction graph $G=(V,E)$; a coalition $S\subseteq V$ is then viable if and only if the induced graph $G[S]$ is connected. The non-emptiness of the core of a coalition game can be tested by a well-known covering LP. Moreover, the integrality gap of its dual packing LP defines exactly the multiplicative least-core an…
We study strong equilibria in symmetric capacitated cost-sharing games. In these games, a graph with designated source $s$ and sink $t$ is given, and each edge is associated with some cost. Each agent chooses strategically an $s$-$t$ path, knowing that the cost of each edge is shared equally between all agents using it. Two variants of cost-sharing games have been previously studied: (i) games where coalitions can form, and (ii) games where edges are associated with capacities; both variants are inspired by real-life scenarios. In this work we combine these variants and analyze strong equilibr…
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…
The formal study of coalition formation in multi-agent systems is typically realized in the framework of hedonic games, which originate from economic theory. The main focus of this branch of research has been on the existence and the computational complexity of deciding the existence of coalition structures that satisfy various stability criteria. The actual process of forming coalitions based on individual behavior has received little attention. In this paper, we study the convergence of simple dynamics leading to stable partitions in a variety of established classes of hedonic games includin…
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, …
Coalition formation is a key topic in multi-agent systems. Coalitions enable agents to achieve goals that they may not have been able to achieve on their own. Previous work has shown problems in coalitional games to be computationally hard. Wooldridge and Dunne (Artificial Intelligence 2006) studied the classical computational complexity of several natural decision problems in Coalitional Resource Games (CRG) - games in which each agent is endowed with a set of resources and coalitions can bring about a set of goals if they are collectively endowed with the necessary amount of resources. The i…
A simple game $(N,v)$ is given by a set $N$ of $n$ players and a partition of $2^N$ into a set $\mathcal{L}$ of losing coalitions $L$ with value $v(L)=0$ that is closed under taking subsets and a set $\mathcal{W}$ of winning coalitions $W$ with $v(W)=1$. Simple games with $α= \min_{p\geq 0}\max_{W\in {\cal W},L\in {\cal L}} \frac{p(L)}{p(W)}<1$ are known as weighted voting games. Freixas and Kurz (IJGT, 2014) conjectured that $α\leq \frac{1}{4}n$ for every simple game $(N,v)$. We confirm this conjecture for two complementary cases, namely when all minimal winning coalitions have size $3$ and w…
Cooperative multihop communication can greatly increase network throughput, yet packet forwarding for other nodes involves opportunity and energy cost for relays. Thus one of the pre-requisite problems in the successful implementation of multihop transmission is how to foster cooperation among selfish nodes. Existing researches mainly adopt monetary stimulating. In this manuscript, we propose instead a simple and self-enforcing forwarding incentive scheme free of indirect monetary remunerating for asymmetric (uplink multihop, downlink single-hop) cellar network based on coalitional game theory…
Motivated by the markets operating on fast time scales, we present a framework for online coalitional games with time-varying coalitional values and propose real-time payoff distribution mechanisms. Specifically, we design two online distributed algorithms to track the Shapley value and the core, the two most widely studied payoff distribution criteria in coalitional game theory. We show that the payoff distribution trajectory resulting from our proposed algorithms converges to a neighborhood of the time-varying solutions. We adopt an operator-theoretic perspective to show the convergence of o…
We consider N-player non-zero sum games played on finite trees (i.e., sequential games), in which the players have the right to repeatedly update their respective strategies (for instance, to improve the outcome wrt to the current strategy profile). This generates a dynamics in the game which may eventually stabilise to a Nash Equilibrium (as with Kukushkin's lazy improvement), and we argue that it is interesting to study the conditions that guarantee such a dynamics to terminate. We build on the works of Le Roux and Pauly who have studied extensively one such dynamics, namely the Lazy Improve…
