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19
Learning Efficient Nash Equilibria in Distributed Systems
, 2010
"... Abstract. An individual’s learning rule is completely uncoupled if it does not depend on the actions or payoffs of anyone else. We propose a variant of log linear learning that is completely uncoupled and that selects an efficient pure Nash equilibrium in all generic nperson games that possess at l ..."
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Cited by 15 (1 self)
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Abstract. An individual’s learning rule is completely uncoupled if it does not depend on the actions or payoffs of anyone else. We propose a variant of log linear learning that is completely uncoupled and that selects an efficient pure Nash equilibrium in all generic nperson games that possess at least one pure Nash equilibrium. In games that do not have such an equilibrium, there is a simple formula that expresses the longrun probability of the various disequilibrium states in terms of two factors: i) the sum of payoffs over all agents, and ii) the maximum payoff gain that results from a unilateral deviation by some agent. This welfare/stability tradeoff criterion provides a novel framework for analyzing the selection of disequilibrium as well as equilibrium states in nperson games. JEL: C72, C73 1 1. Learning equilibrium in complex interactive systems Game theory has traditionally focussed on situations that involve a small number of players. In these environments it makes sense to assume that players know the structure of the game and can predict the strategic behavior of their opponents. But there are many situations involving huge numbers of players where these assumptions are not particularly persuasive.
Aspiration learning in coordination games
 in IEEE Conference on Decision and Control
, 2010
"... Abstract — We consider the problem of distributed convergence to efficient outcomes in coordination games through payoffbased learning dynamics, namely aspiration learning. The proposed learning scheme assumes that players reinforce well performed actions, by successively playing these actions, oth ..."
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Abstract — We consider the problem of distributed convergence to efficient outcomes in coordination games through payoffbased learning dynamics, namely aspiration learning. The proposed learning scheme assumes that players reinforce well performed actions, by successively playing these actions, otherwise they randomize among alternative actions. Our first contribution is the characterization of the asymptotic behavior of the induced Markov chain of the iterated process by an equivalent finitestate Markov chain, which simplifies previously introduced analysis on aspiration learning. We then characterize explicitly the behavior of the proposed aspiration learning in a generalized version of socalled coordination games, an example of which is network formation games. In particular, we show that in coordination games the expected percentage of time that the efficient action profile is played can become arbitrarily large. I.
Game Theory and Distributed Control
, 2012
"... Game theory has been employed traditionally as a modeling tool for describing and influencing behavior in societal systems. Recently, game theory has emerged as a valuable tool for controlling or prescribing behavior in distributed engineered systems. The rationale for this new perspective stems fro ..."
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Cited by 3 (1 self)
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Game theory has been employed traditionally as a modeling tool for describing and influencing behavior in societal systems. Recently, game theory has emerged as a valuable tool for controlling or prescribing behavior in distributed engineered systems. The rationale for this new perspective stems from the parallels between the underlying decision making architectures in both societal systems and distributed engineered systems. In particular, both settings involve an interconnection of decision making elements whose collective behavior depends on a compilation of local decisions that are based on partial information about each other and the state of the world. Accordingly, there is extensive work in game theory that is relevant to the engineering agenda. Similarities notwithstanding, there remain important differences between the constraints and objectives in societal and engineered systems that require looking at game theoretic methods from a new perspective. This chapter provides an overview of selected recent developments of game theoretic methods in this role as a framework for distributed control in engineered systems.
Achieving pareto optimal equilibria in energy efficient clustered ad hoc networks
 in Military Communication Conference, Milcom
, 2012
"... Abstract—In this paper, a decentralized iterative algorithm, namely the optimal dynamic learning (ODL) algorithm, is analysed. The ability of this algorithm of achieving a Pareto optimal working point exploiting only a minimal amount of information is shown. The algorithm performance is analysed in ..."
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Cited by 3 (2 self)
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Abstract—In this paper, a decentralized iterative algorithm, namely the optimal dynamic learning (ODL) algorithm, is analysed. The ability of this algorithm of achieving a Pareto optimal working point exploiting only a minimal amount of information is shown. The algorithm performance is analysed in a clustered ad hoc network, where radio devices are assumed to operate above a minimal signal to interference plus noise ratio (SINR) threshold while minimizing the global power consumption. Sufficient analytical conditions for ODL to converge to the desired working point are provided, moreover through numerical simulations the ability of the algorithm to configure an interference limited network is shown. The performances of ODL and of a Nash equilibrium reaching algorithm are numerically compared, and their performance as a function of available resources is studied. The gain of ODL is shown to be larger when the amount of available radio resources is scarce.
CORASMA Program on Cognitive Radio for Tactical Networks: High Fidelity Simulator and First Results on Dynamic Frequency Allocation
"... Abstract—This paper reports some preliminary results of the “cognitive radio for dynamic spectrum management” (CORASMA) program that is dedicated to the evaluation of cognitive solutions for tactical wireless networks. It presents two main aspects of the program: the simulator and the cognitive solu ..."
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Abstract—This paper reports some preliminary results of the “cognitive radio for dynamic spectrum management” (CORASMA) program that is dedicated to the evaluation of cognitive solutions for tactical wireless networks. It presents two main aspects of the program: the simulator and the cognitive solutions proposed by the authors. The first part is dedicated to the simulator. We explain the rationale used to design its architecture, and how this architecture allows to assess and compare different cognitive solutions in an operational context. The second part addresses the dynamic frequency allocation topic that is part of the cognitive solutions tackled in the program CORASMA. We first give an overview of the challenges attached to this problem in the military context and then we expose the technical solutions studied by the authors for this purpose. Finally, we present some results obtained from the simulator as an illustration. I.
Information Management in the Smart Grid: A Learning Game Approach
, 2013
"... In this article, the smart grid is modeled as a decentralized and hierarchical network, made of three categories of agents: producers, providers and microgrids. To optimize their decisions concerning the energy prices and the traded quantities of energy, the agents need to forecast the energy produc ..."
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In this article, the smart grid is modeled as a decentralized and hierarchical network, made of three categories of agents: producers, providers and microgrids. To optimize their decisions concerning the energy prices and the traded quantities of energy, the agents need to forecast the energy productions and the demand of the microgrids. The biases resulting from the decentralized learning might create imbalances between demand and supply, leading to penalties for the providers and for the producers. We determine analytically prices that provide to the producers a guarantee to avoid such penalties, reporting all the risk on the providers. Additionally, we prove that collaborative learning, through a grand coalition of providers where information is shared and forecasts aligned on a single value, minimizes their average risk. Simulations, run on a toy network, lead us to observe that the convergence rates of the collaborative learning strategy are clearly superior to rates resulting from distributed learning, using external and internal regret minimization.
Learning in Games
"... Abstract—In a Nash equilibrium, each player selects a strategy that is optimal with respect to the strategies of other players. This definition does not mention the process by which players reach a Nash equilibrium. The topic of learning in games seeks to address this issue in that it explores how s ..."
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Abstract—In a Nash equilibrium, each player selects a strategy that is optimal with respect to the strategies of other players. This definition does not mention the process by which players reach a Nash equilibrium. The topic of learning in games seeks to address this issue in that it explores how simplistic learning/adaptation rules can lead to Nash equilibrium. This article presents a selective sampling of learning rules and their longrun convergence properties, i.e., conditions under which player strategies converge or not to Nash equilibrium.
c ○ 2013 Society for Industrial and Applied Mathematics ASPIRATION LEARNING IN COORDINATION GAMES ∗
"... Abstract. We consider the problem of distributed convergence to efficient outcomes in coordination games through dynamics based on aspiration learning. Our first contribution is the characterization of the asymptotic behavior of the induced Markov chain of the iterated process in terms of an equival ..."
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Abstract. We consider the problem of distributed convergence to efficient outcomes in coordination games through dynamics based on aspiration learning. Our first contribution is the characterization of the asymptotic behavior of the induced Markov chain of the iterated process in terms of an equivalent finitestate Markov chain. We then characterize explicitly the behavior of the proposed aspiration learning in a generalized version of coordination games, examples of which include network formation and commonpool games. In particular, we show that in generic coordination games the frequency at which an efficient action profile is played can be made arbitrarily large. Although convergence to efficient outcomes is desirable, in several coordination games, such as commonpool games, attainability of fair outcomes, i.e., sequences of plays at which players experience highly rewarding returns with the same frequency, might also be of special interest. To this end, we demonstrate through analysis and simulations that aspiration learning also establishes fair outcomes in all symmetric coordination games, including commonpool games.
Author manuscript, published in "ICC 2013, Budapest: Hungary (2013)" DOI: 10.1109/ICC.2013.6654723 Achieving Pareto Optimal Equilibria in Energy Efficient Clustered Ad Hoc Networks
, 2014
"... Abstract—In this paper, a decentralized iterative algorithm, namely the optimal dynamic learning (ODL) algorithm, is analysed. The ability of this algorithm of achieving a Pareto optimal working point exploiting only a minimal amount of information is shown. The algorithm performance is analysed in ..."
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Abstract—In this paper, a decentralized iterative algorithm, namely the optimal dynamic learning (ODL) algorithm, is analysed. The ability of this algorithm of achieving a Pareto optimal working point exploiting only a minimal amount of information is shown. The algorithm performance is analysed in a clustered ad hoc network, where radio devices are assumed to operate above a minimal signal to interference plus noise ratio (SINR) threshold while minimizing the global power consumption. Sufficient analytical conditions for ODL to converge to the desired working point are provided, moreover through numerical simulations the ability of the algorithm to configure an interference limited network is shown. The performances of ODL and of a Nash equilibrium reaching algorithm are numerically compared, and their performance as a function of available resources is studied. The gain of ODL is shown to be larger when the amount of available radio resources is scarce.