A distributed asynchronous solver for Nash Equilibria in hypergraphical games

Hypergraphical games provides a compact model of a network of self-interested agents, each involved in simultaneous subgames with its neighbors. The overall aim is for the agents in the network to reach a Nash Equilibrium, in which no agent has an incentive to change their response, but without revealing all their private information. Asymmetric Distributed constraint satisfaction (ADisCSP) has been proposed as a solution to this search problem. In this paper, we propose a new model of hypergraphical games as an ADisCSP based on a new global constraint, and a new asynchronous algorithm for solving ADisCSP that is able to find a Nash Equilibrium. We show empirically that we significantly reduce both message passing and computation time, achieving an order of magnitude improvement in messaging and in non-concurrent computation time on dense problems compared to state-of-the art algorithms

Coalition Formation For Distributed Constraint Optimization Problems

This dissertation presents our research on coalition formation for Distributed Constraint Optimization Problems (DCOP). In a DCOP, a problem is broken up into many disjoint sub-problems, each controlled by an autonomous agent and together the system of agents have a joint goal of maximizing a global utility function. In particular, we study the use of coalitions for solving distributed k-coloring problems using iterative approximate algorithms, which do not guarantee optimal results, but provide fast and economic solutions in resource constrained environments. The challenge in forming coalitions using iterative approximate algorithms is in identifying constraint dependencies between agents that allow for effective coalitions to form. We first present the Virtual Structure Reduction (VSR) Algorithm and its integration with a modified version of an iterative approximate solver. The VSR algorithm is the first distributed approach for finding structural relationships, called strict frozen pairs, between agents that allows for effective coalition formation. Using coalition structures allows for both more efficient search and higher overall utility in the solutions. Secondly, we relax the assumption of strict frozen pairs and allow coalitions to form under a probabilistic relationship. We identify probabilistic frozen pairs by calculating the propensity between two agents, or the joint probability of two agents in a k-coloring problem having the same value in all satisfiable instances. Using propensity, we form coalitions in sparse graphs where strict frozen pairs may not exist, but there is still benefit to forming coalitions. Lastly, we present a cooperative game theoretic approach where agents search for Nash stable coalitions under the conditions of additively separable and symmetric value functions

Quasi-Nash Equilibria for Non-Convex Distributed Power Allocation Games in Cognitive Radios

In this paper, we consider a sensing-based spectrum sharing scenario in cognitive radio networks where the overall objective is to maximize the sum-rate of each cognitive radio user by optimizing jointly both the detection operation based on sensing and the power allocation, taking into account the influence of the sensing accuracy and the interference limitation to the primary users. The resulting optimization problem for each cognitive user is non-convex, thus leading to a non-convex game, which presents a new challenge when analyzing the equilibria of this game where each cognitive user represents a player. In order to deal with the non-convexity of the game, we use a new relaxed equilibria concept, namely, quasi-Nash equilibrium (QNE). A QNE is a solution of a variational inequality obtained under the first-order optimality conditions of the player's problems, while retaining the convex constraints in the variational inequality problem. In this work, we state the sufficient conditions for the existence of the QNE for the proposed game. Specifically, under the so-called linear independent constraint qualification, we prove that the achieved QNE coincides with the NE. Moreover, a distributed primal-dual interior point optimization algorithm that converges to a QNE of the proposed game is provided in the paper, which is shown from the simulations to yield a considerable performance improvement with respect to an alternating direction optimization algorithm and a deterministic game

Telekommunikaatiomarkkinoita kuvaavan mallin Nashin tasapainon laskeminen erilaisilla kognitiiviradion skenaarioilla

In this thesis we are investigating how the different cognitive radio scenarios affect the operators, the customers and the government. We have constructed a telecommunication market model to find out the consequences. We have constructed a two-stage game based on this model. In the first stage operators buy capacity. That means licensing spectrum and maintaining the network technology. In the second stage the operators set prices to their service. The special properties in our game are limited availability of capacity and uncertainty of demand. The limited availability of capacity is simulated by using a quadratic cost function. The uncertainty of demand is generated by adding a random variable to the demand function. The main theme of this thesis is comparing different scenarios to each other. For each scenario we developed functions to represent the additional capacity. Finally we compare the results by using indexes created to represent the utility of different sides. Solving the game is started by using analytical methods with general number of players. However, the complexity of dependencies prevents solving game analytically. We continue with numerical methods. With numerical methods we primarily are searching pure strategy Nash equilibrium. It turns out that pure strategy equilibrium does not exist generally. To solve mixed strategy equilibrium, we form a normal form game to region that our algorithm keeps oscillating and solve its mixed strategy equilibrium. According to the results of this thesis, one of the suggested changes in rules would be equally profitable for operators, but remarkably better by the government's and the customers' point of view.Tässä työssä tutkittiin kognitiivisen radion erilaisten toteutusskenaarioiden vaikutuksia operaattoreiden, asiakkaiden sekä valtion kannalta. Työssä rakennettiin malli kuvaamaan telekommunikaatiomarkkinoita. Mallin pohjalta tehdään peli, joka koostuu kahdesta vaiheesta. Ensimmäisessä vaiheessa operaattorit hankkivat kapasiteettia, eli ostavat lisenssin spektriin sekä huoltavat verkkoa ylläpitävää tekniikkaa. Toisessa vaiheessa operaattorit hinnoittelevat palvelunsa. Rakentamassamme pelissä erikoispiirteinä ovat kapasiteetin rajallinen saatavuus sekä kysynnän epätarkka ennustettavuus. Kapasiteetin rajallisuutta simuloidaan sen neliöllisellä kustannusfunktiolla. Liian tarkan ennustettavuuden poistamiseksi kysyntäfunktioon on lisätty satunnaismuuttuja. Työn tarkoitus on erilaisten sääntöjen vertailu keskenään. Erilaisia skenaarioita varten on rakennettu omat funktiot kuvaamaan lisäkapasiteetin saamista. Lopuksi tuloksia vertaillaan eri osapuolien näkökulmista näiden tyytyväisyyttä kuvaamaan kehitettyjen indeksien avulla. Työssä pelin ratkaisu aloitetaan analyyttisillä menetelmillä yleisellä pelaajamäärällä. Ongelmaksi kuitenkin muodostuu liian monimutkaiset riippuvuudet, jotka estävät pelin analyyttisen ratkaisemisen. Pelin tutkimista jatketaan numeerisilla menetelmillä. Numeerisella menetelmällä haetaan ensisijaisesti puhtaista strategioista koostuvaa Nashin tasapainoa. Osoittautuu kuitenkin, että aina puhtaiden strategioiden tasapainoa ei ole olemassa. Sekastrategiatasapainon ratkaisemiseksi muodostamme matriisipelin alueelle, johon algoritmimme jää kiertämään kehää. Lopuksi ratkaistaan toisella algoritmilla sen sekastrategiatasapaino. Työn tulosten perusteella toinen ehdotetuista sääntömuutoksista olisi operaattoreiden tuottojen kannalta nykytilanteen kanssa yhtä hyvä, mutta valtion ja asiakkaiden kannalta selvästi nykytilannetta parempi

Fast optimization methods for machine learning, and game-theoretic models of cultural evolution

This thesis has two parts. In the first part, we explore fast stochastic optimization methods for machine learning. Mathematical optimization is a backbone of modern machine learning. Most machine learning problems require optimizing some objective function that measures how well a model matches a data set, with the intention of drawing patterns and making decisions on new unseen data. The success of optimization algorithms in solving these problems is critical to the success of machine learning, and has enabled the research community to explore more complex machine learning problems that require bigger models and larger datasets. Stochastic gradient descent (SGD) has become the standard optimization routine in machine learning, and in particular in deep neural networks, due to its impressive performance across a wide variety of tasks and models. SGD, however, can often be slow for neural networks with many layers and typically requires careful user oversight for setting hyperparameters properly. While innovations such as batch normalization and skip connections have helped alleviate some of these issues, why such innovations are required eludes full understanding, and it is worthwhile to gain deeper theoretical insights into these problems and to consider more advanced optimization methods specifically tailored towards training large complex models. In this part of the thesis, we review and analyze some of the recent progress made in this direction, and develop new optimization algorithms that are provably fast, significantly easier to train, and require less user oversight. Then, we will discuss the theory of quantized networks, which use low-precision weights to compress and accelerate neural networks, and when/why they are trainable. Finally, we discuss some recent results on how the convergence of SGD is affected by the architecture of neural nets, and we show using theoretical analysis that wide networks train faster than narrow nets, and deeper networks train slower than shallow nets - an effect often observed in practice. In the second part of the thesis, we study the evolution of cultural norms in human societies using game-theoretic models, drawing from research in cross-cultural psychology. Understanding human behavior and modeling how cultural norms evolve in different human societies is vital for designing policies and avoiding conflicts around the world. In this part, we explore ways to use computational game-theoretic techniques, and in particular evolutionary game-theoretic (EGT) models, to gain insight into why different human societies have different norms and behaviors. We first describe an evolutionary game-theoretic model to study how norms change in a society, based on the idea that different strength of norms in societies translate to different game-theoretic interaction structures and incentives. We identify conditions that determine when societies change their existing norms, when they are resistant to such change, and how this depends on the strength of norms in a society. Next, we extend this study to analyze the evolutionary relationships between the tendency to conform and how quickly a population reacts when conditions make a change in norm desirable. Our analysis identifies conditions when a tipping point is reached in a population, causing norms to change rapidly. Next we study conditions that affect the existence of group-biased behavior among humans (i.e., favoring others from the same group, and being hostile towards others from different groups). Using an evolutionary game-theoretic model, we show that out-group hostility is dramatically reduced by mobility. Technological and societal advances over the past centuries have greatly increased the degree to which humans change physical locations, and our results show that in highly mobile societies, one's choice of action is more likely to depend on what individual one is interacting with, rather than the group to which the individual belongs

Architectures and algorithms for dynamic overlay networks

Most of today’s Internet of Things (IoT) applications assume that data will be moved offdevices into centralized cloud platforms. While existing IoT systems leverage cloud-based analytics for meaningful data reasoning, the assumption that data should always be moved off the devices is problematic. The amount of data to be moved from devices over Internet gateways to cloud platforms is huge which potentially make it cost inefficient. In other scenarios, privacy concerns of customers or organizational rules complicate the process of transferring data to third-party data centers.This dissertation proposes architectures and dynamic overlay network algorithms for in-networkand edge processing of data offered by the globally available IoT devices and provides a global platform for meaningful and responsive data analysis and decision making. The proposed techniques shift IoT analytics from a ”collect data now and analyze it later” scenario to directlyproviding meaningful information from the in-network processing of devices data at or near thedevices. The techniques serve future IoT use cases including distributed context awareness, on-demand data analysis, and in-network decision making. The dissertation comprises three main components.The first component is a device management protocol for cloning devices’ data in proximateEdge Computing platforms. Unlike existing application-layer IoT management protocols theproposed protocol uses the LTE LTE-A radio frame structure, device-to-device communication,and IoT data properties to avoid excessive network access latency in existing technologies.The second component realizes distributed IoT analytics as overlay networks of devices clones. By means of virtual network embedding, it selects and interconnects devices’ clones to efficiently realize applications’ virtual topologies to achieve goals such as minimum latency, minimum infrastructure cost, or maximum infrastructure utilization.Finally, the dissertation presents a communication middleware that allows autonomous discovery, self-deployment, and online migration of devices’ clones across heterogeneous Edge computing platforms. The middleware ensures that communication latency between clones is kept minimum despite the uncontrolled variability of the network and hosting platforms conditions.We evaluate the proposed architectures and algorithms through simulations and prototypeimplementation of various components in controlled testbed environments, which we evaluateusing real user applications. We explore the feasibility of the proposed techniques from boththeoretical and practical perspectives.Keywords: Cloud Computing, Internet of Things, Algorithmic Game Theory, Compressive Sensin

On Influence, Stable Behavior, and the Most Influential Individuals in Networks: A Game-Theoretic Approach

We introduce a new approach to the study of influence in strategic settings where the action of an individual depends on that of others in a network-structured way. We propose \emph{influence games} as a \emph{game-theoretic} model of the behavior of a large but finite networked population. Influence games allow \emph{both} positive and negative \emph{influence factors}, permitting reversals in behavioral choices. We embrace \emph{pure-strategy Nash equilibrium (PSNE)}, an important solution concept in non-cooperative game theory, to formally define the \emph{stable outcomes} of an influence game and to predict potential outcomes without explicitly considering intricate dynamics. We address an important problem in network influence, the identification of the \emph{most influential individuals}, and approach it algorithmically using PSNE computation. \emph{Computationally}, we provide (a) complexity characterizations of various problems on influence games; (b) efficient algorithms for several special cases and heuristics for hard cases; and (c) approximation algorithms, with provable guarantees, for the problem of identifying the most influential individuals. \emph{Experimentally}, we evaluate our approach using both synthetic influence games as well as several real-world settings of general interest, each corresponding to a separate branch of the U.S. Government. \emph{Mathematically,} we connect influence games to important game-theoretic models: \emph{potential and polymatrix games}.Comment: Accepted to AI Journal, subject to addressing the reviewers' points (which are addressed in this version). An earlier version of the article appeared in AAAI-1