Theory Of Nonzero-sum Games Research Articles

Optimized control for human-multi-robot collaborative manipulation via multi-player Q-learning

In this paper, optimized interaction control is investigated for human-multi-robot collaboration control problems, which cannot be described by the traditional impedance controller. To realize global optimized interaction performance, the multi-player non-zero sum game theory is employed to obtain the optimized interaction control of each robot agent. Regarding the game strategies, Nash equilibrium strategy is utilized in this paper. In human-multi-robot collaboration problems, the dynamics parameters of the human arm and the manipulated object are usually unknown. To obviate the dependence on these parameters, the multi-player Q-learning method is employed. Moreover, for the human-multi-robot collaboration problem, the optimized solution is difficult to resolve due to the existence of the desired reference position. A multi-player Nash Q-learning algorithm considering the desired reference position is proposed to deal with the problem. The validity of the proposed method is verified through simulation studies.

Towards a Light Weight Routing Security in IoT Using Non-cooperative Game Models and Dempster–Shaffer Theory

The internet of things (IoT) has become an emerging technology owing to the rapidly increasing number of devices and their connectivity to the internet. Routing protocol for low-power and lossy networks (RPL) is a predominant routing protocol for the IoT. The RPL routing embraces the distance to the gateway node as a rank for parent selection and builds the destination oriented directed acyclic graph (DODAG). The malicious nodes utilize the advantage of low rank based parent selection to involve in data forwarding. However, the malicious node behavior and the harsh channel conditions due to the collision are equally considered as malicious in the existing detection mechanisms. In addition, most of the routing solutions exploit the traditional schemes for IoT security, but not considering the adaptability to IoT routing specifications. Thus, this work attempts to integrate the DODAG-specific contextual trust model, and RPL-specific rank variance factor, named as Secure RPL using non-cooperative game MOdels and DEmpster Shaffer Theory in IoT (S-MODEST), such that it can detect the attackers accurately and significantly reduces the resource consumption. The non-cooperative game model consists of two interrelated formulations in the proposed solution. Firstly, non-zero sum game constructs the trust model and extracts the contextual information from DODAG structure to strengthen the trustworthiness. Secondly, the evolutionary game is utilized for trusted router selection. The non-zero sum game theory formulates the interaction of nodes and assists the trust measurement by applying direct and restricted Dempster–Shaffer theory. The DODAG-specific contextual trust evaluation differentiates the collision dropping from the undesirable scenarios and supports the nodes in building a highly trusted DODAG structure to the gateway using multiplicative trust factor. To enforce the routing cooperation of selfish nodes and differentiate malicious nodes, the evolutionary game model embraces the node trust, which is measured using non-zero sum game model. As a result, the non-cooperative game models enable the S-MODEST to precisely select a secure route as well as to maintain the routing performance effectively. The simulation results demonstrate that the detection accuracy and throughput of the proposed context-aware noncooperative game theory based trust model are substantially higher and outperform the existing SecTrust.

Adaptive optimal tracking controls of unknown multi-input systems based on nonzero-sum game theory

This paper focuses on the optimal tracking control problem (OTCP) for the unknown multi-input system by using a reinforcement learning (RL) scheme and nonzero-sum (NZS) game theory. First, a generic method for the OTCP of multi-input systems is formulated with steady-state controls and optimal feedback controls based on the NZS game theory. Then a three-layer neural network (NN) identifier is introduced to approximate the unknown system, and the input dynamics are obtained by using the derivative of the identifier. To transform the OTCP into a regulation optimal problem, an augmentation of the multi-input system is constructed by using the tracking error and the commanded trajectory. Moreover, we use an NN-based RL method to online learn the optimal value functions of all the inputs, which are then directly used to calculate the optimal tracking controls. All the NN weights are tuned synchronously online with a newly introduced adaptation based on the estimation error. The convergence of the NN weights and the stability of the closed-loop system are analyzed. Finally, a two-motor driven servo system and another nonlinear system are presented to illustrate the feasibility of the algorithm for both linear and nonlinear multi-input systems.

Distribution Design of Two Rival Decenteralized Supply Chains: a Two-person Nonzero Sum Game Theory Approach

We consider competition between two decentralized supply chains network under demand uncertainty. Each chain consists of one risk-averse manufacturer and a group of risk-averse retailers. These two chains present substitutable products to the geographical dispensed markets. The markets’ demands are contingent upon prices, service levels, and advertising efforts of two supply chains. We formulate the distribution design problem of two rival chains as a two-person nonzero sum game. Since strategic decisions of distribution designs often have priority over tactical ones, we first calculate the equilibrium of tactical decisions for each pair of distribution design scenarios. Then, according to the presented methodology, we find Nash equilibrium solutions of distribution network scenarios for two rival chains. Eventually, the research has concluded with a numerical example in order to illustrate the real applications of the methodology.

The Passage of the Civil Service Reforms Act of 1978, and the Business and the Union: A Non-Zero Sum Game

The paper seeks to use non-zero sum bargaining theory to analyze the Civil Service Reforms Act of 1978. President Carter believed that business practices can be used in federal bureaucracy to improve the efficiency and productivity in the government. The Carter Administration sought very actively the cooperation of the business and the labor union to pass the reforms. Both the labor union and the business groups bargained intensely to preserve and promote their interests in the reforms. Based on archival data from the President Jimmy Carter Library, this paper analyzes the bargaining position of the labor union and the business groups from the non-zero sum game theory to offer a different perspective on the passage of the Civil Service Reforms Act of 1978.

Game theory in sugarcane crop residue and available energy optimization

This work proposes a mathematical model to aid variety selection and planting quantity of sugarcane in order to reduce crop residues, maximize energy generated by this residue, and satisfy all the supply of the mill. We propose Linear Programming with two objective. The conflict between these objectives allows the use of the Nonzero-sum Game Theory.

A Nash game approach to mixed H/sub 2//H/sub ∞/ control

The established theory of nonzero sum games is used to solve a mixed H/sub 2//H/sub /spl infin//, control problem. Our idea is to use the two pay-off functions associated with a two-player Nash game to represent the H/sub 2/ and H/sub /spl infin// criteria separately. We treat the state-feedback problem and we find necessary and sufficient conditions for the existence of a solution. Both the finite and infinite time problems are considered. In the infinite horizon case we present a full stability analysis. The resulting controller is a constant state-feedback law, characterized by the solution to a pair of cross-coupled Riccati equations, which may be solved using a standard numerical integration procedure. We begin our development by considering strategy sets containing linear controllers only. At the end of the paper we broaden the strategy sets to include a class of nonlinear controls. It turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Correlated relaxed equilibria in nonzero-sum linear differential games

Intrinsic to the theory of nonzero-sum games is an underlying desire among players to form some cooperation, which in no-sense is a binding contract. This notion of cooperation without compulsion requires either initiation by a third party or some form of preplay communication. In a seminal paper [l], Aumann introduced one such scheme for normal form (matrix) games, called correlation in randomized strategies. Correlated equilibria are, in some sense, extensions of Nash equilibrium solutions. The advantages of using correlated equilibria in matrix games are many. They form a compact convex set for any matrix game and can be computed via linear programming methods. Very often some correlated equilibria yield higher expected payoffs for all players compared to Nash equilibrium payoffs (see [I, 11, 121 for details). Some interesting variations and extensions of Aumann’s approach to correlation in nonzero-sum games are included in [7, 111 and some applications to economic theory can be found, for example, in [9]. In this paper we define correlated strategies for differential games and introduce a solution concept, which is inspired by Moulin’s approach to correlated equilibria [9, 11, 121. We consider linear differential games of prescribed duration. In this section we assume that the players receive no information about the state variables during the play, except for their initial values which are common knowledge from the start. Hence, open-loop strategies are considered. Our correlation scheme is based on relaxed control theory. In Section 3, we also discuss correlated equilibria in closed-loop strategies. Let .N= { 1, 2, . . . . m} be the set of players. Consider an m-person linear differential nonzero-sum game of prescribed duration with 104 0022-247X/92 $3.00

A note on the strategic adoption of a new technology

This note reports an application of two-person, nonzero-sum game theory to a problem in the economics of technology adoption. It extends the analysis of a previous paper to consider differentiable mixed-strategy equilibria. In this case, the mixed-strategy equilibrium has a natural interpretation as a pure strategy equilibrium in an appropriately defined differential game.

A note on linear-quadratic pursuit-evasion differential games

An interpretation of the zero-sum, two-person, linear-quadratic differential game is provided via the bargaining and threat theory of nonzerosum games.