Routing Games with Progressive Filling

Max-min fairness (MMF) is a widely known approach to a fair allocation of bandwidth to each of the users in a network. This allocation can be computed by uniformly raising the bandwidths of all users without violating capacity constraints. We consider an extension of these allocations by raising the bandwidth with arbitrary and not necessarily uniform time-depending velocities (allocation rates). These allocations are used in a game-theoretic context for routing choices, which we formalize in progressive filling games (PFGs). We present a variety of results for equilibria in PFGs. We show that these games possess pure Nash and strong equilibria. While computation in general is NP-hard, there are polynomial-time algorithms for prominent classes of Max-Min-Fair Games (MMFG), including the case when all users have the same source-destination pair. We characterize prices of anarchy and stability for pure Nash and strong equilibria in PFGs and MMFGs when players have different or the same source-destination pairs. In addition, we show that when a designer can adjust allocation rates, it is possible to design games with optimal strong equilibria. Some initial results on polynomial-time algorithms in this direction are also derived

CSMA Local Area Networking under Dynamic Altruism

In this paper, we consider medium access control of local area networks (LANs) under limited-information conditions as befits a distributed system. Rather than assuming "by rule" conformance to a protocol designed to regulate packet-flow rates (e.g., CSMA windowing), we begin with a non-cooperative game framework and build a dynamic altruism term into the net utility. The effects of altruism are analyzed at Nash equilibrium for both the ALOHA and CSMA frameworks in the quasistationary (fictitious play) regime. We consider either power or throughput based costs of networking, and the cases of identical or heterogeneous (independent) users/players. In a numerical study we consider diverse players, and we see that the effects of altruism for similar players can be beneficial in the presence of significant congestion, but excessive altruism may lead to underuse of the channel when demand is low

Exchange of Services in Networks: Competition, Cooperation, and Fairness

Exchange of services and resources in, or over, networks is attracting nowadays renewed interest. However, despite the broad applicability and the extensive study of such models, e.g., in the context of P2P networks, many fundamental questions regarding their properties and efficiency remain unanswered. We consider such a service exchange model and analyze the users' interactions under three different approaches. First, we study a centrally designed service allocation policy that yields the fair total service each user should receive based on the service it others to the others. Accordingly, we consider a competitive market where each user determines selfishly its allocation policy so as to maximize the service it receives in return, and a coalitional game model where users are allowed to coordinate their policies. We prove that there is a unique equilibrium exchange allocation for both game theoretic formulations, which also coincides with the central fair service allocation. Furthermore, we characterize its properties in terms of the coalitions that emerge and the equilibrium allocations, and analyze its dependency on the underlying network graph. That servicing policy is the natural reference point to the various mechanisms that are currently proposed to incentivize user participation and improve the efficiency of such networked service (or, resource) exchange markets.Comment: to appear in ACM Sigmetrics 201

Strong Nash Equilibria in Games with the Lexicographical Improvement Property

We introduce a class of finite strategic games with the property that every deviation of a coalition of players that is profitable to each of its members strictly decreases the lexicographical order of a certain function defined on the set of strategy profiles. We call this property the Lexicographical Improvement Property (LIP) and show that it implies the existence of a generalized strong ordinal potential function. We use this characterization to derive existence, efficiency and fairness properties of strong Nash equilibria. We then study a class of games that generalizes congestion games with bottleneck objectives that we call bottleneck congestion games. We show that these games possess the LIP and thus the above mentioned properties. For bottleneck congestion games in networks, we identify cases in which the potential function associated with the LIP leads to polynomial time algorithms computing a strong Nash equilibrium. Finally, we investigate the LIP for infinite games. We show that the LIP does not imply the existence of a generalized strong ordinal potential, thus, the existence of SNE does not follow. Assuming that the function associated with the LIP is continuous, however, we prove existence of SNE. As a consequence, we prove that bottleneck congestion games with infinite strategy spaces and continuous cost functions possess a strong Nash equilibrium

Channel assignment and routing in cooperative and competitive wireless mesh networks

This thesis was submitted for the degree of Docter of Philosophy and awarded by Brunel University.In this thesis, the channel assignment and routing problems have been investigated for both cooperative and competitive Wireless Mesh networks (WMNs). A dynamic and distributed channel assignment scheme has been proposed which generates the network topologies ensuring less interference and better connectivity. The proposed channel assignment scheme is capable of detecting the node failures and mobility in an efficient manner. The channel monitoring module precisely records the quality of bi-directional links in terms of link delays. In addition, a Quality of Service based Multi-Radio Ad-hoc On Demand Distance Vector (QMR-AODV) routing protocol has been devised. QMR-AODV is multi-radio compatible and provides delay guarantees on end-to-end paths. The inherited problem of AODV’s network wide flooding has been solved by selectively forwarding the routing queries on specified interfaces. The QoS based delay routing metric, combined with the selective route request forwarding, reduces the routing overhead from 24% up to 36% and produces 40.4% to 55.89% less network delays for traffic profiles of 10 to 60 flows, respectively. A distributed channel assignment scheme has been proposed for competitive WMNs, where the problem has been investigated by applying the concepts from non-cooperative bargaining Game Theory in two stages. In the first stage of the game, individual nodes of the non-cooperative setup is considered as the unit of analysis, where sufficient and necessary conditions for the existence of Nash Equilibrium (NE) and Negotiation-Proof Nash Equilibrium (N-PNE) have been derived. A distributed algorithm has been presented with perfect information available to the nodes of the network. In the presence of perfect information, each node has the knowledge of interference experience by the channels in its collision domain. The game converges to N-PNE in finite time and the average fairness achieved by all the nodes is greater than 0.79 (79%) as measured through Jain Fairness Index. Since N-PNE and NE are not always a system optimal solutions when considered from the end-nodes prospective, the model is further extended to incorporate non-cooperative end-users bargaining between two end user’s Mesh Access Points (MAPs), where an increase of 10% to 27% in end-to-end throughput is achieved. Furthermore, a non-cooperative game theoretical model is proposed for end-users flow routing in a multi-radio multi-channel WMNs. The end user nodes are selfish and compete for the channel resources across the WMNs backbone, aiming to maximize their own benefit without taking care for the overall system optimization. The end-to-end throughputs achieved by the flows of an end node and interference experienced across the WMNs backbone are considered as the performance parameters in the utility function. Theoretical foundation has been drawn based on the concepts from the Game Theory and necessary conditions for the existence of NE have been extensively derived. A distributed algorithm running on each end node with imperfect information has been implemented to assess the usefulness of the proposed mechanism. The analytical results have proven that a pure strategy Nash Equilibrium exists with the proposed necessary conditions in a game of imperfect information. Based on a distributed algorithm, the game converges to a stable state in finite time. The proposed game theoretical model provides a more reasonable solution with a standard deviation of 2.19Mbps as compared to 3.74Mbps of the random flow routing. Finally, the Price of Anarchy (PoA) of the system is close to one which shows the efficiency of the proposed scheme.The Higher Education Commission of Pakistan and the University of Engineering and Technology, Peshawar