We study balanced solutions for network bargaining games with general capacities, where agents can participate in a fixed but arbitrary number of contracts. We provide the first polynomial time algorithm for computing balanced solutions for these games. In addition, we prove that an instance has a balanced solution if and only if it has a stable one. Our methods use a new idea of reducing an instance with general capacities to a network bargaining game with unit capacities defined on an auxiliary graph. This represents a departure from previous approaches, which rely on computing an allocation in the intersection of the core and prekernel of a corresponding cooperative game, and then proving that the solution corresponding to this allocation is balanced. In fact, we show that such cooperative game methods do not extend to general capacity games, since contrary to the case of unit capacities, there exist allocations in the intersection of the core and prekernel with no corresponding balanced solution. Finally, we identify two sufficient conditions under which the set of balanced solutions corresponds to the intersection of the core and prekernel, thereby extending the class of games for which this result was previously known.
Bargaining networks model the behavior of a set of players that need to reach pairwise agreements for making profits. Nash bargaining solutions are special outcomes of such games that are both stable and balanced. Kleinberg and Tardos proved a sharp algorithmic characterization of such outcomes, but left open the problem of how the actual bargaining process converges to them. A partial answer was provided by Azar et al. who proposed a distributed algorithm for constructing Nash bargaining solutions, but without polynomial bounds on its convergence rate. In this paper, we introduce a simple and…
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 are represented by weighted edges in our bipartite network. Each agent in the market is additionally limited by a capacity representing the number of contracts which he or she may undertake. When all agents are limited to just one contract each, prior research applied natural generalizations of the Nash bargaining solution to the networked setting, defined the…
We consider a one-sided assignment market or exchange network with transferable utility and propose a model for the dynamics of bargaining in such a market. Our dynamical model is local, involving iterative updates of 'offers' based on estimated best alternative matches, in the spirit of pairwise Nash bargaining. We establish that when a balanced outcome (a generalization of the pairwise Nash bargaining solution to networks) exists, our dynamics converges rapidly to such an outcome. We extend our results to the cases of (i) general agent 'capacity constraints', i.e., an agent may be allowed to…
We consider a dynamical system for computing Nash bargaining solutions on graphs and focus on its rate of convergence. More precisely, we analyze the edge-balanced dynamical system by Azar et al and fully specify its convergence for an important class of elementary graph structures that arise in Kleinberg and Tardos' procedure for computing a Nash bargaining solution on general graphs. We show that all these dynamical systems are either linear or eventually become linear and that their convergence times are quadratic in the number of matched edges.
Bargaining networks model social or economic situations in which agents seek to form the most lucrative partnership with another agent from among several alternatives. There has been a flurry of recent research studying Nash bargaining solutions (also called 'balanced outcomes') in bargaining networks, so that we now know when such solutions exist, and also that they can be computed efficiently, even by market agents behaving in a natural manner. In this work we study a generalization of Nash bargaining, that models the possibility of unequal 'bargaining powers'. This generalization was introd…
We study decentralized markets with the presence of middlemen, modeled by a non-cooperative bargaining game in trading networks. Our goal is to investigate how the network structure of the market and the role of middlemen influence the market's efficiency and fairness. We introduce the concept of limit stationary equilibrium in a general trading network and use it to analyze how competition among middlemen is influenced by the network structure, how endogenous delay emerges in trade and how surplus is shared between producers and consumers.
The unprecedented growth of mobile data traffic challenges the performance and economic viability of today's cellular networks, and calls for novel network architectures and communication solutions. Data offloading through third-party WiFi or femtocell access points (APs) can effectively alleviate the cellular network congestion in a low operational and capital expenditure. This solution requires the cooperation and agreement of mobile cellular network operators (MNOs) and AP owners (APOs). In this paper, we model and analyze the interaction among one MNO and multiple APOs (for the amount of M…
We study trade networks with a tree structure, where a seller with a single indivisible good is connected to buyers, each with some value for the good, via a unique path of intermediaries. Agents in the tree make multiplicative revenue share offers to their parent nodes, who choose the best offer and offer part of it to their parent, and so on; the winning path is determined by who finally makes the highest offer to the seller. In this paper, we investigate how these revenue shares might be set via a natural bargaining process between agents on the tree, specifically, egalitarian bargaining be…
We study a network extension to the Nash bargaining game, as introduced by Kleinberg and Tardos (STOC'08), where the set of players corresponds to vertices in a graph $G=(V,E)$ and each edge $ij\in E$ represents a possible deal between players $i$ and $j$. We reformulate the problem as a cooperative game and study the following question: Given a game with an empty core (i.e. an unstable game) is it possible, through minimal changes in the underlying network, to stabilize the game? We show that by removing edges in the network that belong to a blocking set we can find a stable solution in polyn…
This paper considers dyadic-exchange networks in which individual agents autonomously form coalitions of size two and agree on how to split a transferable utility. Valid results for this game include stable (if agents have no unilateral incentive to deviate), balanced (if matched agents obtain similar benefits from collaborating), or Nash (both stable and balanced) outcomes. We design provably-correct continuous-time algorithms to find each of these classes of outcomes in a distributed way. Our algorithmic design to find Nash bargaining solutions builds on the other two algorithms by having th…
Simultaneously information and power transfer in mobile relay networks have recently emerged, where the relay can harvest the radio frequency (RF) energy and then use this energy for data forwarding and system operation. Most of the previous works do not consider that the relay may have its own objectives, such as using the harvested energy for its own transmission instead of maximizing transmission of the network. Therefore, in this paper, we propose a Nash bargaining approach to balance the information transmission efficiency of source-destination pairs and the harvested energy of the relay …
Split learning (SL) is an emergent distributed learning framework which can mitigate the computation and wireless communication overhead of federated learning. It splits a machine learning model into a device-side model and a server-side model at a cut layer. Devices only train their allocated model and transmit the activations of the cut layer to the server. However, SL can lead to data leakage as the server can reconstruct the input data using the correlation between the input and intermediate activations. Although allocating more layers to a device-side model can reduce the possibility of d…
Negotiation is a process where agents aim to work through disputes and maximize their surplus. As the use of deep reinforcement learning in bargaining games is unexplored, this paper evaluates its ability to exploit, adapt, and cooperate to produce fair outcomes. Two actor-critic networks were trained for the bidding and acceptance strategy, against time-based agents, behavior-based agents, and through self-play. Gameplay against these agents reveals three key findings. 1) Neural agents learn to exploit time-based agents, achieving clear transitions in decision preference values. The Cauchy di…
This paper investigates the incentives of mobile network operators (MNOs) for acquiring additional spectrum to offer mobile virtual network operators (MVNOs) and thereby inviting competition for a common pool of end users (EUs). We consider interactions between two service providers, an MNO and an MVNO, when the EUs 1) must choose one of them 2) have the option to defect to an outside option should the SP duo offer unsatisfactory access fees or qualities of service. We formulate a multi-stage hybrid of cooperative bargaining and non-cooperative games in which the two SPs jointly determine thei…
In the context of networking, research has focused on non-cooperative games, where the selfish agents cannot reach a binding agreement on the way they would share the infrastructure. Many approaches have been proposed for mitigating the typically inefficient operating points. However, in a growing number of networking scenarios selfish agents are able to communicate and reach an agreement. Hence, the degradation of performance should be considered at an operating point of a cooperative game. Accordingly, our goal is to lay foundations for the application of cooperative game theory to fundament…
We consider the impact of incomplete information on incentives for node cooperation in parallel relay networks with one source node, one destination node, and multiple relay nodes. All nodes are selfish and strategic, interested in maximizing their own profit instead of the social welfare. We consider the practical situation where the channel state on any given relay path is not observable to the source or to the other relays. We examine different bargaining relationships between the source and the relays, and propose a framework for analyzing the efficiency loss induced by incomplete informat…
Bargaining games on exchange networks have been studied by both economists and sociologists. A Balanced Outcome for such a game is an equilibrium concept that combines notions of stability and fairness. In a recent paper, Kleinberg and Tardos introduced balanced outcomes to the computer science community and provided a polynomial-time algorithm to compute the set of such outcomes. Their work left open a pertinent question: are there natural, local dynamics that converge quickly to a balanced outcome? In this paper, we provide a partial answer to this question by showing that simple edge-balanc…
A network game assigns a level of collectively generated wealth to every network that can form on a given set of players. A variable network game combines a network game with a network formation probability distribution, describing certain restrictions on network formation. Expected levels of collectively generated wealth and expected individual payoffs can be formulated in this setting. We investigate properties of the resulting expected wealth levels as well as the expected variants of well-established network game values as allocation rules that assign to every variable network game a payof…
Millimeter wave channels suffer from considerable degradation in the channel quality when the signal is Non Line of Sight (NLOS) between the source and the destination. Multihop relaying is thus anticipated to improve the communi- cation between a source and its destination. This is achieved by transmitting the signal to a sequence of relays in which a Line of Sight (LOS) signal exists between two nodes along the path, or more generally when the signal is better than the transmitted signal directly from the source to the destination. In this paper, we consider a millimeter wave network compose…
Information-centric networking extensively uses universal in-network caching. However, developing an efficient and fair collaborative caching algorithm for selfish caches is still an open question. In addition, the communication overhead induced by collaboration is especially poorly understood in a general network setting such as realistic ISP and Autonomous System networks. In this paper, we address these two problems by modeling the in-network caching problem as a Nash bargaining game. We show that the game is a convex optimization problem and further derive the corresponding distributed alg…
