Parallel computing as a congestion game

Game-theoretical approach to the analysis of parallel algorithms is proposed. The approach is based on presentation of the parallel computing as a congestion game. In the game processes compete for resources such as core of a central processing unit and a communication subsystem. There are players, resources and payoffs (time delays) of players which depend on resources usage. Comparative analysis of various optimality principles in the proposed model may be performed

Distributed Spectrum Access for Cognitive Small Cell Networks: A Robust Graphical Game Approach

This letter investigates the problem of distributed spectrum access for cognitive small cell networks. Compared with existing work, two inherent features are considered: i) the transmission of a cognitive small cell base station only interferes with its neighbors due to the low power, i.e., the interference is local, and ii) the channel state is time-varying due to fading. We formulate the problem as a robust graphical game, and prove that it is an ordinal potential game which has at least one pure strategy Nash equilibrium (NE). Also, the lower throughput bound of NE solutions is analytically obtained. To cope with the dynamic and incomplete information constraints, we propose a distribute spectrum access algorithm to converge to some stable results. Simulation results validate the effectiveness of the proposed game-theoretic distributed learning solution in time-varying spectrum environment.Comment: 7 pages, 5 figures, Submitted to IEEE Transactions on Vehicular Technology as a correspondenc

Load-aware Dynamic Spectrum Access for Small Cell Networks: A Graphical Game Approach

In this letter, we investigate the problem of dynamic spectrum access for small cell networks, using a graphical game approach. Compared with existing studies, we take the features of different cell loads and local interference relationship into account. It is proved that the formulated spectrum access game is an exact potential game with the aggregate interference level as the potential function, and Nash equilibrium (NE) of the game corresponds to the global or local optima of the original optimization problem. A lower bound of the achievable aggregate interference level is rigorously derived. Finally, we propose an autonomous best response learning algorithm to converge towards its NE. It is shown that the proposed game-theoretic solution converges rapidly and its achievable performance is close to the optimum solution.Comment: 6 pages, 5 figures, Submitted to IEEE Transactions on Vehicular Technology as a correspondence (under third round review

Distributed Nash Equilibrium Seeking by A Consensus Based Approach

In this paper, Nash equilibrium seeking among a network of players is considered. Different from many existing works on Nash equilibrium seeking in non-cooperative games, the players considered in this paper cannot directly observe the actions of the players who are not their neighbors. Instead, the players are supposed to be capable of communicating with each other via an undirected and connected communication graph. By a synthesis of a leader-following consensus protocol and the gradient play, a distributed Nash equilibrium seeking strategy is proposed for the non-cooperative games. Analytical analysis on the convergence of the players' actions to the Nash equilibrium is conducted via Lyapunov stability analysis. For games with non-quadratic payoffs, where multiple isolated Nash equilibria may coexist in the game, a local convergence result is derived under certain conditions. Then, a stronger condition is provided to derive a non-local convergence result for the non-quadratic games. For quadratic games, it is shown that the proposed seeking strategy enables the players' actions to converge to the Nash equilibrium globally under the given conditions. Numerical examples are provided to verify the effectiveness of the proposed seeking strategy

A Unified Strategy for Solution Seeking in Graphical N-coalition Noncooperative Games

This paper aims to reduce the communication and computation costs of the Nash equilibrium seeking strategy for the $N$-coalition noncooperative games proposed in [1]. The objective is achieved in two manners: 1. An interference graph is introduced to describe the interactions among the agents in each coalition. 2. The Nash equilibrium seeking strategy is designed with the interference graphs considered. The convergence property of the proposed Nash equilibrium seeking strategy is analytically investigated. It is shown that the agents' actions generated by the proposed method converge to a neighborhood of the Nash equilibrium of the graphical $N$-coalition noncooperative games under certain conditions. Several special cases where there is only one coalition and/or there are coalitions with only one agent are considered. The results for the special cases demonstrate that the proposed seeking strategy achieves the solution seeking for noncooperative games, social cost minimization problems and single-agent optimization problems in a unified framework. Numerical examples are presented to support the theoretical results

Revisiting Optimal Power Control: its Dual Effect on SNR and Contention

In this paper we study a transmission power tune problem with densely deployed 802.11 Wireless Local Area Networks (WLANs). While previous papers emphasize on tuning transmission power with either PHY or MAC layer separately, optimally setting each Access Point's (AP's) transmission power of a densely deployed 802.11 network considering its dual effects on both layers remains an open problem. In this work, we design a measure by evaluating impacts of transmission power on network performance on both PHY and MAC layers. We show that such an optimization problem is intractable and then we investigate and develop an analytical framework to allow simple yet efficient solutions. Through simulations and numerical results, we observe clear benefits of the dual-effect model compared to solutions optimizing solely on a single layer; therefore, we conclude that tuning transmission power from a dual layer (PHY-MAC) point of view is essential and necessary for dense WLANs. We further form a game theoretical framework and investigate above power-tune problem in a strategic network. We show that with decentralized and strategic users, the Nash Equilibrium (N.E.) of the corresponding game is in-efficient and thereafter we propose a punishment based mechanism to enforce users to adopt the social optimal strategy profile under both perfect and imperfect sensing environments

Approximate Best-Response Dynamics in Random Interference Games

In this paper we develop a novel approach to the convergence of Best-Response Dynamics for the family of interference games. Interference games represent the fundamental resource allocation conflict between users of the radio spectrum. In contrast to congestion games, interference games are generally not potential games. Therefore, proving the convergence of the best-response dynamics to a Nash equilibrium in these games requires new techniques. We suggest a model for random interference games, based on the long term fading governed by the players' geometry. Our goal is to prove convergence of the approximate best-response dynamics with high probability with respect to the randomized game. We embrace the asynchronous model in which the acting player is chosen at each stage at random. In our approximate best-response dynamics, the action of a deviating player is chosen at random among all the approximately best ones. We show that with high probability, with respect to the players' geometry and asymptotically with the number of players, each action increases the expected social-welfare (sum of achievable rates). Hence, the induced sum-rate process is a submartingale. Based on the Martingale Convergence Theorem, we prove convergence of the strategy profile to an approximate Nash equilibrium with good performance for asymptotically almost all interference games. We use the Markovity of the induced sum-rate process to provide probabilistic bounds on the convergence time. Finally, we demonstrate our results in simulated examples

Distributed Spectrum Access with Spatial Reuse

Efficient distributed spectrum sharing mechanism is crucial for improving the spectrum utilization. The spatial aspect of spectrum sharing, however, is less understood than many other aspects. In this paper, we generalize a recently proposed spatial congestion game framework to design efficient distributed spectrum access mechanisms with spatial reuse. We first propose a spatial channel selection game to model the distributed channel selection problem with fixed user locations. We show that the game is a potential game, and develop a distributed learning mechanism that converges to a Nash equilibrium only based on users' local observations. We then formulate the joint channel and location selection problem as a spatial channel selection and mobility game, and show that it is also a potential game. We next propose a distributed strategic mobility algorithm, jointly with the distributed learning mechanism, that can converge to a Nash equilibrium

Low-Complexity Distributed Radio Access Network Slicing: Algorithms and Experimental Results

Radio access network (RAN) slicing is an effective methodology to dynamically allocate networking resources in 5G networks. One of the main challenges of RAN slicing is that it is provably an NP-Hard problem. For this reason, we design near-optimal low-complexity distributed RAN slicing algorithms. First, we model the slicing problem as a congestion game, and demonstrate that such game admits a unique Nash equilibrium (NE). Then, we evaluate the Price of Anarchy (PoA) of the NE, i.e., the efficiency of the NE as compared to the social optimum, and demonstrate that the PoA is upper-bounded by 3/2. Next, we propose two fully-distributed algorithms that provably converge to the unique NE without revealing privacy-sensitive parameters from the slice tenants. Moreover, we introduce an adaptive pricing mechanism of the wireless resources to improve the network owner's profit. We evaluate the performance of our algorithms through simulations and an experimental testbed deployed on the Amazon EC2 cloud, both based on a real-world dataset of base stations from the OpenCellID project. Results conclude that our algorithms converge to the NE rapidly and achieve near-optimal performance, while our pricing mechanism effectively improves the profit of the network owner

Spatial Spectrum Access Game

A key feature of wireless communications is the spatial reuse. However, the spatial aspect is not yet well understood for the purpose of designing efficient spectrum sharing mechanisms. In this paper, we propose a framework of spatial spectrum access games on directed interference graphs, which can model quite general interference relationship with spatial reuse in wireless networks. We show that a pure Nash equilibrium exists for the two classes of games: (1) any spatial spectrum access games on directed acyclic graphs, and (2) any games satisfying the congestion property on directed trees and directed forests. Under mild technical conditions, the spatial spectrum access games with random backoff and Aloha channel contention mechanisms on undirected graphs also have a pure Nash equilibrium. We also quantify the price of anarchy of the spatial spectrum access game. We then propose a distributed learning algorithm, which only utilizes users' local observations to adaptively adjust the spectrum access strategies. We show that the distributed learning algorithm can converge to an approximate mixed-strategy Nash equilibrium for any spatial spectrum access games. Numerical results demonstrate that the distributed learning algorithm achieves up to superior performance improvement over a random access algorithm.Comment: The paper has been accepted by IEEE Transactions on Mobile Computin