Game Theory with Engineering Applications

Bauso, Dario

doi:10.1137/1.9781611974287

Cited by 66 publications

(29 citation statements)

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“…We will also discuss methods for specialized dynamic games, such as linear-quadratic games [29][30][31][32][33][34], potential games [35][36][37][38][39][40], and zero-sum games [41,42]. Finally, we will discuss general methods based on Pontryagin's Maximum Principle [1,2,4,43]. These existing methods for games suffer from different reasons when applied to nonlinear dynamic games or only handle special cases.…”

Section: Literature Surveymentioning

confidence: 99%

“…The standard solution method for an OLNE is via Pontryagin's Minimum Principle (PMP) for either continuous or discrete-time problems, as recognized by the community [1][2][3][4][5]43,56]. Although the PMP allows us to analyze the existence of solution and solve for analytical solutions for a few simple games, the resulting boundary value problem (BVP) with optimization is, in general, hard to solve [1].…”

Section: Literature Surveymentioning

confidence: 99%

“…Such games arise when multiple agents with differing objectives act upon one same dynamic system. The system can be naturally discrete-time or emerge from discretization of a differential game [2][3][4][5]. Dynamic games have many applications including pursuit-evasion [6], active-defense [7,8], economics [9] and the smart grid [10] .…”

Section: Introductionmentioning

confidence: 99%

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Newton’s Method and Differential Dynamic Programming for Unconstrained Nonlinear Dynamic Games

Lamperski

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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Dynamic games arise when multiple agents with differing objectives choose control a dynamic system. They model a wide variety of applications in economics, defense, energy systems and etc. However, compared to single-agent control problems, the computational methods for dynamic games are relatively limited. As in the single-agent case, only specific dynamic games can be solved exactly, and so approximation algorithms are required. In this paper, we show how to extend a recursive Newton's algorithm and the popular differential dynamic programming (DDP) for single-agent optimal control to the case of full-information non-zero sum dynamic games. In the singleagent case, convergence of DDP is proved by comparison with Newton's method, which converges locally at a quadratic rate. We show that the iterates of Newton's method and DDP are sufficiently close for the DDP to inherit the quadratic convergence rate of Newton's method. We also prove both methods result in an open-loop Nash equilibrium and a local feedback O(ε 2 )-Nash equilibrium. Numerical examples are provided.

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Section: Literature Surveymentioning

confidence: 99%

Section: Literature Surveymentioning

confidence: 99%

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Newton’s Method and Differential Dynamic Programming for Unconstrained Nonlinear Dynamic Games

Lamperski

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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“…The discussion is deliberately brief, given the many texts on the topic of game theory directed at different audiences, including economists (1,5,6), computer scientists (7)(8)(9), and engineers (10)(11)(12).…”

Section: Basic Concepts and Notationmentioning

confidence: 99%

Game Theory and Control

Marden

Shamma

2018

Annu. Rev. Control Robot. Auton. Syst.

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Game theory is the study of decision problems in which there are multiple decision makers and the quality of a decision maker's choice depends on both that choice and the choices of others. While game theory has been studied predominantly as a modeling paradigm in the mathematical social sciences, there is a strong connection to control systems in that a controller can be viewed as a decision-making entity. Accordingly, game theory is relevant in settings with multiple interacting controllers. This article presents an introduction to game theory, followed by a sampling of results in three specific control theory topics where game theory has played a significant role: (a) zero-sum games, in which the two competing players are a controller and an adversarial environment; (b) team games, in which several controllers pursue a common goal but have access to different information; and (c) distributed control, in which both a game and online adaptive rules are designed to enable distributed interacting subsystems to achieve a collective objective.

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“…Game theory is the study of conflicts and cooperation among rational decision makers [48], and has been used to describe customers' behaviors in DR in recent studies [36]. In the proposed DR scheme, each customer rationally and selfishly chooses a DR strategy to maximize their own welfare, while the total DR rebate is limited.…”

Section: Formulation Of Non-cooperative Gamementioning

confidence: 99%

A Novel Distributed Large-Scale Demand Response Scheme in High Proportion Renewable Energy Sources Integration Power Systems

Fan

Jia

et al. 2018

Applied Sciences

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Large-scale demand response (DR) is a useful regulatory method used in high proportion renewable energy sources (RES) integration power systems. Current incentive-based DR schemes are unsuitable for large-scale DR due to their centralized formulation. This paper proposes a distributed scheme to support large-scale implementation of DR. To measure DR performance, this paper proposes the customer directrix load (CDL), which is a desired load profile, to replace the customer baseline load (CBL). The uniqueness of CDL makes it more suitable for distributed schemes, while numerous CBLs have to be calculated in a centralized manner to ensure fairness. To allocate DR tasks and rebates, this paper proposes a distributed approach, where the load serving entity (LSE) only needs to publish a total rebate and corresponding CDL. As for each customer, s/he needs to claim an ideal rebate ratio that ranges from 0 to 1, which indicates the proportion of rebate s/he wants to get from LSE. The rebate value for each customer also determines his or her DR task. Then, the process of customer claims for the ideal rebate ratio is modeled as a non-cooperative game, and the Nash equilibrium is proved to exist. The Gossip algorithm is improved in this paper to be suitable for socially connected networks, and the entire game process is distributed. Finally, a large-scale DR system is formulated. The simulation results show that the proposed DR can promote the consumption of RES. Additionally, this scheme is suitable for large-scale customer systems, and the distributed game process is effective.

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Game Theory with Engineering Applications

Cited by 66 publications

References 0 publications

Newton’s Method and Differential Dynamic Programming for Unconstrained Nonlinear Dynamic Games

Newton’s Method and Differential Dynamic Programming for Unconstrained Nonlinear Dynamic Games

Game Theory and Control

A Novel Distributed Large-Scale Demand Response Scheme in High Proportion Renewable Energy Sources Integration Power Systems

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