Optimal Reverse Carpooling Over Wireless Networks - A Distributed Optimization Approach

We focus on a particular form of network coding, reverse carpooling, in a wireless network where the potentially coded transmitted messages are to be decoded immediately upon reception. The network is fixed and known, and the system performance is measured in terms of the number of wireless broadcasts required to meet multiple unicast demands. Motivated by the structure of the coding scheme, we formulate the problem as a linear program by introducing a flow variable for each triple of connected nodes. This allows us to have a formulation polynomial in the number of nodes. Using dual decomposition and projected subgradient method, we present a decentralized algorithm to obtain optimal routing schemes in presence of coding opportunities. We show that the primal sub-problem can be expressed as a shortest path problem on an \emph{edge-graph}, and the proposed algorithm requires each node to exchange information only with its neighbors.Comment: submitted to CISS 201

Multiagent Maximum Coverage Problems: The Trade-off Between Anarchy and Stability

The price of anarchy and price of stability are three well-studied performance metrics that seek to characterize the inefficiency of equilibria in distributed systems. The distinction between these two performance metrics centers on the equilibria that they focus on: the price of anarchy characterizes the quality of the worst-performing equilibria, while the price of stability characterizes the quality of the best-performing equilibria. While much of the literature focuses on these metrics from an analysis perspective, in this work we consider these performance metrics from a design perspective. Specifically, we focus on the setting where a system operator is tasked with designing local utility functions to optimize these performance metrics in a class of games termed covering games. Our main result characterizes a fundamental trade-off between the price of anarchy and price of stability in the form of a fully explicit Pareto frontier. Within this setup, optimizing the price of anarchy comes directly at the expense of the price of stability (and vice versa). Our second results demonstrates how a system-operator could incorporate an additional piece of system-level information into the design of the agents' utility functions to breach these limitations and improve the system's performance. This valuable piece of system-level information pertains to the performance of worst performing agent in the system.Comment: 14 pages, 4 figure

A Comprehensive Survey of Potential Game Approaches to Wireless Networks

Potential games form a class of non-cooperative games where unilateral improvement dynamics are guaranteed to converge in many practical cases. The potential game approach has been applied to a wide range of wireless network problems, particularly to a variety of channel assignment problems. In this paper, the properties of potential games are introduced, and games in wireless networks that have been proven to be potential games are comprehensively discussed.Comment: 44 pages, 6 figures, to appear in IEICE Transactions on Communications, vol. E98-B, no. 9, Sept. 201

Incentive-Based Control of Asynchronous Best-Response Dynamics on Binary Decision Networks

Various populations of interacting decision-making agents can be modeled by asynchronous best-response dynamics, or equivalently, linear threshold dynamics. Building upon recent convergence results in the absence of control, we now consider how such a network can be efficiently driven to a desired equilibrium state by offering payoff incentives or rewards for using a particular strategy, either uniformly or targeted to individuals. We begin by showing that strategy changes are monotone following an increase in payoffs in coordination games, and that the resulting equilibrium is unique. Based on these results, for the case when a uniform incentive is offered to all agents, we show how to compute the optimal incentive using a binary search algorithm. When different incentives can be offered to each agent, we propose a new algorithm to select which agents should be targeted based on maximizing a ratio between the cascading effect of a strategy switch by each agent and the incentive required to cause the agent to switch. Simulations show that this algorithm computes near-optimal targeted incentives for a wide range of networks and payoff distributions in coordination games and can also be effective for anti-coordination games

Potential games and competitive scheduling in wireless networks

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 121-125).This thesis studies a game theoretic model for scheduling transmissions among multiple self-interested users in a wireless network with fading. Our model involves a finite number of mobile users transmitting to a common base station under time-varying channel conditions. A distinguishing feature of our model is the assumption that the channel quality of each user is affected by global and time-varying conditions at the base station, resulting in each user observing a common channel state. Each user chooses a transmission policy that maximizes its utility function, which captures a natural trade-off between throughput and power. The transmission policy specifies how transmissions should be scheduled as a function of the time-varying common channel state observed by each user. We make three main contributions. First, we establish the existence of a Nash equilibrium of this game and characterize the set of equilibria. We investigate the efficiency properties of these equilibria, and study a related aggregate utility maximization problem, to serve as a benchmark for the performance of the equilibria. We quantify the efficiency loss in the game comparing the optimal solution of the aggregate utility maximization problem, to the best and worst equilibria in terms of the aggregate utility. We show that the performance of the worst equilibrium can be arbitrarily bad (in terms of the aggregate utility), but the efficiency loss of the best equilibrium can be bounded as a function of a technology-related parameter. Our second contribution is to study various distributed mechanisms to reach an equilibrium of this game.(cont.) We use the theory of potential games to establish convergence of such mechanisms to an equilibrium. To this end, we study conditions under which the scheduling game is a potential game. This necessitates extending the known necessary conditions for the existence of ordinal potential in games. In this thesis, we show that the scheduling game has a twice continuously differentiable ordinal potential if and only if a rate alignment condition holds. In our third contribution, we investigate the related question of characterizing the "distance" of an arbitrary game to an exact potential game. We provide a new framework based on combinatorial Hodge theory for projecting an arbitrary game to the set of exact potential games. We prove that the equilibria of a game are equilibria of its projection, where E is bounded by the projection error. Moreover, we show that the projection of a game to the set of exact potential games can be calculated using distributed consensus algorithms.by Utku Ozan Candogan.S.M

The Price of Selfishness in Network Coding

A game-theoretic framework is introduced for studying selfish user behavior in shared wireless networks. The investigation treats an n-unicast problem in a wireless network that employs a restricted form of network coding called reverse carpooling. Unicast sessions independently choose routes through the network. The cost of a set of unicast routes is the number of wireless transmissions required to establish those connections using those routes. Game theory is employed as a tool for analyzing the impact of cost sharing mechanisms on the global system performance when each unicast independently and selfishly chooses its route to minimize its individual cost. The investigation focuses on the performance of stable solutions, where a stable solution is one in which no single unicast can improve its individual cost by changing its route. The results include bounds on the best- and worst-case stable solutions compared to the best performance that could be found and implemented using a centralized controller. The optimal cost sharing protocol is derived and the worst-case solution is bounded. That worst-case stable performance cannot be improved using cost-sharing protocols that are independent of the network structure