We consider stochastic dynamic games in large population conditions where multiclass agents are weakly coupled via their individual dynamics and costs.We approach this game problem by the so-called Nash Certainty Equivalence (NCE) Principle which leads to a decentralized control synthesis.The McKean-Vlasov NCE method presented paper has close connection with statistical physics of particle systems: both identify consistency relationship between agent (or particle) at microscopic level mass...

We consider linear quadratic Gaussian (LQG) games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs. A state aggregation technique is developed obtain a set of decentralized control laws for individuals which possesses an epsiv-Nash equilibrium property. stability property mass behavior established, effect inaccurate statistics on isolated agent also analyzed by variational techniques.

This paper considers the coordination and consensus of networked agents where each agent has noisy measurements its neighbors' states. For seeking, we propose stochastic approximation-type algorithms with a decreasing step size, introduce notions mean square strong consensus. Although size reduces detrimental effect noise, it also ability algorithm to drive individual states towards other. The key technique is ensure trade-off for rate size. By following this strategy, first develop double...

We consider uplink power control for lognormal fading channels in the large population case. First, we examine structure of law a centralized stochastic optimal setup. analyze effect populations on individual inputs. Next, split cost to approach problem game theoretic framework. In this context, introduce an auxiliary LQG system and resulting /spl epsiv/-Nash equilibrium law; subsequently generalize methodology developed wireless get approximation collective all other users given user. The...

We consider linear-quadratic-Gaussian (LQG) games with a major player and large number of minor players. The has significant influence on others. players individually have negligible impact, but they collectively contribute mean field coupling terms in the individual dynamics costs. To overcome dimensionality difficulty obtain decentralized strategies, so-called Nash certainty equivalence methodology is applied. control synthesis preceded by state space augmentation via set aggregate...

In cognitive radio (CR) networks, secondary users can cooperatively sense the spectrum to detect presence of primary users. this paper, we propose a fully distributed and scalable cooperative spectrum-sensing scheme based on recent advances in consensus algorithms. proposed scheme, maintain coordination only local information exchange without centralized common receiver. Unlike most existing decision rules, such as or-rule or 1-out-of-N rule, use make final decision. Simulation results show...

We study a class of linear-quadratic-Gaussian (LQG) control problems with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> decision makers, where the basic objective is to minimize social cost as sum individual costs containing mean field coupling. The exact socially optimal solution (determining particular Pareto optimum) requires centralized information for each agent and has high implementational complexity. As an alternative we...

We consider consensus seeking of networked agents on directed graphs where each agent has only noisy measurements its neighbors' states. Stochastic approximation type algorithms are employed so that the individual states converge both in mean square and almost surely to same limit. further generalize algorithm networks with random link failures prove convergence results.

We consider a mean field linear-quadratic-Gaussian game with major player and large number of minor players parametrized by continuum set. The generated the is approximated random process depending only on initial state Brownian motion player, this leads to two limiting optimal control problems coefficients, which are solved subject consistency requirement approximation. set decentralized strategies constructed from has an $\varepsilon$-Nash equilibrium property when applied but finite...

Game theory can provide a useful tool to study the security problem in mobile ad hoc networks (MANETs). Most of existing works on applying game theories only consider two players model: an attacker and defender. While this assumption may be valid for network with centralized administration, it is not realistic MANETs, where administration available. In paper, using recent advances mean field theory, we propose novel theoretic approach multiple MANETs. The provides powerful mathematical...

Cognitive radios (CRs) have been considered for use in mobile ad hoc networks (MANETs). The area of security Radio MANETs (CR-MANETs) has yet to receive much attention. However, some distinct characteristics CRs introduce new, non-trivial risks CR-MANETs. In this paper, we study spectrum sensing data falsification (SSDF) attacks CR-MANETs, which intruders send false local results cooperative sensing, and SSDF may result incorrect decisions by CRs. We present a consensus-based scheme counter...

Cognitive radios, which are capable of sensing their surrounding environment and adapting internal parameters, have been considered in mobile ad hoc networks. Secondary users can cooperatively sense the spectrum to detect presence primary users. In this article we present a novel biologically inspired consensus-based cooperative scheme CR-MANETs. Our is based on recent advances consensus algorithms that taken inspiration from self-organizing behavior animal groups such as birds, fish, ants,...

The purpose of this paper is to synthesize initial mean consensus behavior a set agents from the fundamental optimization principles i) stochastic dynamic games, and ii) optimal control. In game model each agent seeks minimize its individual quadratic discounted cost function involving states all other agents. formulation we derive limiting infinite population field equation system explicitly compute unique solution. resulting (MF) control strategies drive track overall population's state...

We study large population stochastic dynamic games where each agent assigns individually determined coupling strengths (with possible spatial interpretation) to the states of other agents in its performance function. The mean field methodology yields a set decentralized controls which generates an -Nash equilibrium for size . A key feature approximation (here with localized interactions) is that resulting th individual agent's control law depends on state and precomputable weighted average...

Mean field game theory has been developed largely following two routes. One of them, called the direct approach, starts by solving a large-scale and next derives set limiting equations as population size tends to infinity. The second route is apply mean approximations formalize fixed point problem analyzing best response representative player. This paper addresses connection difference approaches in linear quadratic (LQ) setting. We first introduce an asymptotic solvability notion for which...

We consider stochastic consensus problems in strongly connected directed graph models where each agent has noisy measurements of its neighbors' states. For seeking, we develop approximation type algorithms with a decreasing step size and establish mean square almost sure convergence the agents' states to same limit.

Cooperative spectrum sensing is attracting more attention in cognitive radio networks. This paper proposes a fully distributed consensus-based cooperative scheme to cope with both fixed and random bidirectional connections among secondary users. In the proposed scheme, users can maintain coordination based on only local interactions without centralized common receiver. Moreover, we prove that even inter-connected unreliable communication links, still make an average consensus. Simulation...

We study large population leader-follower stochastic multi-agent systems where the agents have linear dynamics and are coupled via their quadratic cost functions. The of each leader is based on a trade-off between moving toward certain reference trajectory which unknown to followers staying near own centroid. On other hand, react by tracking convex combination centroid leaders. approach this dynamic game problem use so-called Mean Field (MF) linear-quadratic-Gaussian (LQG) control theory. In...

This paper considers both synchronous and asynchronous consensus algorithms with noisy measurements. For stochastic approximation based algorithms, the existing convergence analysis dynamic topologies heavily relies on quadratic Lyapunov functions, whose existence, however, may be difficult to ensure for switching directed graphs. Our main contribution is introduce a new analytical approach. We first show fundamental role of ergodic backward products mean square in additive noise....

Networks are ubiquitous in modern society and the need to analyse, design control them is evident. However many technical social networks apparently grow unboundedly over time. This has undesirable consequence that, inevitably, any method founded upon techniques whose effectiveness decreases with size of network will eventually be overwhelmed. paper presents a framework called Graphon Mean Field Game (GMFG) theory for analysis non-cooperative dynamical game systems distributed unbounded...

The emergence of the graphon theory large networks and their infinite limits has enabled formulation a centralized control dynamical systems distributed on asymptotically (Gao Caines, IEEE CDC 2017, 2018). Furthermore, study decentralized such was initiated in (Caines Huang, 2018, 2019), where Graphon Mean Field Games (GMFG) GMFG equations were formulated for analysis non-cooperative dynamic games unbounded networks. In that work, existence uniqueness results introduced equations, together...