Yuyue Yan

The stability property of the loss-aversion-based noncooperative switched systems with quadratic payoffs is investigated. In this system, each agent adopts the lower sensitivity parameter in the myopic pseudo-gradient dynamics for the case of losing utility than gaining utility, and both system dynamics and switching events (conditions) are depending on agents’ payoff functions. Sufficient conditions under which agents’ state converges toward the Nash equilibrium are derived in accordance with t

In this paper, we connect cognitive hierarchy theory with the pseudo-gradient dynamics in noncooperative systems to extend the pseudo-gradient dynamics with some prediction behaviors under Level- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> thinking. In this framework, each agent believes that he is the most sophisticated person in the noncooperative system and makes the proact

A framework for hierarchical noncooperative systems with dynamic agents is proposed. In the characterized framework, agents in each group are incentivized by a corresponding group manager who represents the benefits of group utility via an intra-group incentive mechanism. The coefficients in intra-group incentive functions are characterized as the group manager's strategy in this paper. The update rules that can be adopted by the group managers are proposed based on the local state and the payof

A zero-sum tax/subsidy approach for stabilizing unstable Nash equilibria in pseudo-gradient-based noncooperative dynamical systems is proposed without the information of agents' personal sensitivity parameters. Specifically, we first present several sufficient conditions for guaranteeing stability of an unstable Nash equilibrium in the face of uncertainty. Furthermore, we develop a framework where a system manager constructs a zero-sum tax/subsidy incentive structure by collecting taxes from som

A new type of bifurcations is illustrated for Nash equilibrium in the noncooperative systems with a squarely bounded state space. In this type of bifurcations, a new Nash equilibrium appears with two new branches, where one of them disappears with the initial branch and the other one holds the same profile as the bifurcation parameter increases. The Nash equilibrium inside the state space is founded as a unstable Nash equilibrium in the noncooperative dynamical system. To improve the efficiency

A zero-sum tax/subsidy approach is proposed to improve the social welfare. In the proposed approach, system designer modifies agents' payoff functions by collecting taxes from some agents and giving the same amount in total as subsidy to a neighbor corresponding agent(s) in the undirected tax/subsidy adjustment graph. Sufficient conditions under which agents' state converges towards the socially maximum state are derived for our proposed approach without using the information of agents' sensitiv

In this letter, we present a structured Kalman filter associated with the transformation matrix for observable Kalman canonical decomposition from conventional Kalman filter (CKF) in order to generate a more accurate time scale. The conventional Kalman filter is a special case of the proposed structured Kalman filter which yields the same predicted unobservable or observable states when some conditions are satisfied. We consider an optimization problem respective to the transformation matrix whe

A Pareto-improving incentive mechanism to improve the weighted social welfare and achieve continual Pareto improvement for a pseudo-gradient-based noncooperative dynamical system is developed. In the proposed approach, the system manager remodels agents' dynamical decision making by collecting taxes from some agents and giving some of the collected taxes to other agents as subsidies with a sustainable budget constraint. Sufficient conditions are derived under which agents' state converges toward

A Pareto improving incentive mechanism is developed to improve the social welfare and achieve continual Pareto improvement for a pseudo-gradient-based noncooperative dynamical system. In the proposed approach, the system manager remodels agents’ dynamical decision making by collecting taxes from some agents and giving some of the collected taxes to other agents as subsidies with a sustainable budget constraint. Sufficient conditions under which agents’ state converges towards the socially maximu

In this paper, we consider the stability problem of Nash equilibrium for a two-agent noncooperative dynamical system with hybrid myopic pseudo-gradient dynamics based on loss-aversion phenomena. In the considered noncooperative dynamical system, each agent adopts different constant sensitivity parameters for the case of losing utilities and gaining utilities. To characterize the stability property, some general characteristics of the active modes and rotational directions are discussed. Based on

A framework for hierarchical noncooperative systems with dynamic agents is proposed. In the characterized framework, agents in each group are incentivized by a corresponding group manager who represents the benefits of group utility via an intra-group incentive mechanism. The coefficients in intra-group incentive functions are characterized as the group manager’s strategy in this paper. The update rules that can be adopted by the group managers are proposed based on local information with contin

To generate accurate time scales, such as national standard time in each country and network time in communication systems, a novel prediction algorithm is proposed for the atomic clock ensembles in which the system is unobservable. In the proposed prediction algorithm, to deal with unobservable state space, we consider a steady-state Kalman filter and an intuitive prediction algorithm to separately treat the observable and unobservable state spaces after Kalman canonical decomposition. It turns

A framework of pseudo-gradient-based noncooperative systems with Level-k thinking under bounded depth of reasoning is proposed. In the characterized framework, each agent believes that he/she is the most sophisticated person in the noncooperative system and is allowed to base their decisions on the predictions about the likely actions of other agents. Depending on a knowledge network of payoff functions, the agents may be able to reasoning the other agents’ best-response states and use these pre