An Optimization and Control Theoretic Approach to Noncooperative Game Design
Tansu Alpcan, Lacra Pavel, Nem Stefanovic
备注：
Earlier versions of this work have appeared partly in the International Conference on Game Theory for Networks (GameNets), in Istanbul, Turkey in May 2009 and Conference on Decision and Control (CDC), Shanghai, China, in December 2009
This paper investigates design of noncooperative games from an optimization and control theoretic perspective. Pricing mechanisms are used as a design tool to ensure that the Nash equilibrium of a fairly general class of noncooperative games satisfies certain global objectives such as welfare maximization or achieving a certain level of quality-of-service (QoS). The class of games considered provide a theoretical basis for decentralized resource allocation and control problems including network congestion control, wireless uplink power control, and optical power control. The game design problem is analyzed under different knowledge assumptions (full versus limited information) and design objectives (QoS versus utility maximization) for separable and non-separable utility functions. The ``price of anarchy'' is shown not to be an inherent feature of full-information games that incorporate pricing mechanisms. Moreover, a simple linear pricing is shown to be sufficient for design of Nash equilibrium according to a chosen global objective for a fairly general class of games. Stability properties of the game and pricing dynamics are studied under the assumption of time-scale separation and in two separate time-scales. Thus, sufficient conditions are derived, which allow the designer to place the Nash equilibrium solution or to guide the system trajectory to a desired region or point. The obtained results are illustrated with a number of examples.
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In some games, additional information hurts a player, e.g., in games with first-mover advantage, the second-mover is hurt by seeing the first-mover's move. What properties of a game determine whether it has such negative "value of information" for a particular player? Can a game have negative value of information for all players? To answer such questions, we generalize the definition of marginal utility of a good to define the marginal utility of a parameter vector specifying a game. So rather than analyze the global structure of the relationship between a game's parameter vector and player be…
COVID-19 is a global epidemic. Till now, there is no remedy for this epidemic. However, isolation and social distancing are seemed to be effective preventive measures to control this pandemic. Therefore, in this paper, an optimization problem is formulated that accommodates both isolation and social distancing features of the individuals. To promote social distancing, we solve the formulated problem by applying a noncooperative game that can provide an incentive for maintaining social distancing to prevent the spread of COVID-19. Furthermore, the sustainability of the lockdown policy is interp…
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A combined base station association and power control problem is studied for the uplink of multichannel multicell cellular networks, in which each channel is used by exactly one cell (i.e., base station). A distributed association and power update algorithm is proposed and shown to converge to a Nash equilibrium of a noncooperative game. We consider network models with discrete mobiles (yielding an atomic congestion game), as well as a continuum of mobiles (yielding a population game). We find that the equilibria need not be Pareto efficient, nor need they be system optimal. To address the lac…
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In the game theory literature, there appears to be little research on equilibrium selection for normal-form games with an infinite strategy space and discontinuous utility functions. Moreover, many existing selection methods are not applicable to games involving both cooperative and noncooperative scenarios (e.g., "games on signed graphs"). With the purpose of equilibrium selection, the power allocation game developed in \cite{allocation}, which is a static, resource allocation game on signed graphs, will be reformulated into an extensive form. Results about the subgame perfect Nash equilibria…
Incentives play an important role in (security and IT) risk management of a large-scale organization with multiple autonomous divisions. This paper presents an incentive mechanism design framework for risk management based on a game-theoretic approach. The risk manager acts as a mechanism designer providing rules and incentive factors such as assistance or subsidies to divisions or units, which are modeled as selfish players of a strategic (noncooperative) game. Based on this model, incentive mechanisms with various objectives are developed that satisfy efficiency, preference-compatibility, an…
We study minimum entropy submodular optimization, a common generalization of the minimum entropy set cover problem, studied earlier by Cardinal et al., and the submodular set cover problem. We give a general bound of the approximation performance of the greedy algorithm using an approach that can be interpreted in terms of a particular type of biased network flows. As an application we rederive known results for the Minimum Entropy Set Cover and Minimum Entropy Orientation problems, and obtain a nontrivial bound for a new problem called the Minimum Entropy Spanning Tree problem. The problem ca…
Shared-constraint games are noncooperative $N$-player games where players are coupled through a common coupling constraint. It is known that such games admit two kinds of equilibria -- generalized Nash equilibria (GNE) and variational equilibria (VE) -- with two different economic interpretations. We consider such games in the context of resource allocation, where players move simultaneously to decide portions of the resource they can consume under a coupling constraint that the sum of the portions they demand be no more than the capacity of the resource. We clarify the worst case and best cas…
Bayesian rationality in strategic games presumes that it is possible to translate strategic uncertainty into imperfect information. Correlated equilibrium is guided by the idea that players are Bayes rational, have a common prior, and choose their strategies independently. I show that an essential condition for Bayesian rationality is violated in every game with imperfect information. Moreover, without strategic uncertainty, players cannot choose their strategies independently. This means strategic independence requires strategic uncertainty. If we distinguish between strategic certainty and u…
A noncooperative game theoretical approach for analysing opportunistic spectrum access (OSA) in cognitive radio (CR) environments is proposed. New concepts from game theory are applied to spectrum access analysis in order to extract rules of behaviour for an emerging environment. In order to assess OSA scenarios of CRs, two oligopoly game models are reformulated in terms of resource access: Cournot and Stackelberg games. Five CR scenes are analysed: simultaneous access of unlicensed users (commons regime) with symmetric and asymmetric costs, with and without bandwidth constraints and sequentia…
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Mechanisms such as auctions and pricing schemes are utilized to design strategic (noncooperative) games for networked systems. Although the participating players are selfish, these mechanisms ensure that the game outcome is optimal with respect to a global criterion (e.g. maximizing a social welfare function), preference-compatible, and strategy-proof, i.e. players have no reason to deceive the designer. The mechanism designer achieves these objectives by introducing specific rules and incentives to the players; in this case by adding resource prices to their utilities. In auction-based mechan…
In this paper, the interactions and energy exchange decisions of a number of geographically distributed storage units are studied under decision-making involving end-users. In particular, a noncooperative game is formulated between customer-owned storage units where each storage unit's owner can decide on whether to charge or discharge energy with a given probability so as to maximize a utility that reflects the tradeoff between the monetary transactions from charging/discharging and the penalty from power regulation. Unlike existing game-theoretic works which assume that players make their de…
Exit-and-Join Dynamics and Equilibrium in Continuum Cooperative Games
Department of Electrical and Computer Engineering（电气与计算机工程系）；New York University Tandon School of Engineering（纽约大学塔恩工程学院）；Brooklyn, NY, USA（布鲁克林，纽约，美国）
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Outsourcing integrated circuit (IC) manufacturing to offshore foundries has grown exponentially in recent years. Given the critical role of ICs in the control and operation of vehicular systems and other modern engineering designs, such offshore outsourcing has led to serious security threats due to the potential of insertion of hardware trojans - malicious designs that, when activated, can lead to highly detrimental consequences. In this paper, a novel game-theoretic framework is proposed to analyze the interactions between a hardware manufacturer, acting as attacker, and an IC testing facili…
