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The inverse Stackelberg game is as common and significant as Nash games and has found its applications in many fields such as economics and mechanism design. However, it is admittedly difficult to solve equilibrium of general inverse Stackelberg game or to analyse it. One way to study the game is to find the team solution first, or equally to study the incentive design problem. This paper explores...
The problem of using input and output sequences to determine the current state of logical dynamical systems has applications in many fields such as systems biology, sequential logic circuits, finite-strategic dynamical noncooperative games, and etc., and has been widely investigated during the recent years. There is an algorithm for verifying whether all sufficiently long input sequences determine...
This paper investigates the modeling and control of networked evolutionary games based on prisoner's dilemma game with punishment strategy. The networked evolutionary game is expressed as a logical dynamic system and then converted into its algebraic form relying on the matrix expression of logic and the method of semi - tensor product of matrices. Next, based on the algebraic form, the dynamic behavior...
Controlling complex systems to desired states is a paramount importance in science and engineering. In this paper, we consider a class of control systems based on non-cooperative dynamical games which can give some light on this kind of complex systems. It involves a hierarchal decision making structure: one leader and multiple followers. The deterministic systems have been studied in the authors'...
In this paper, the stability of finite evolutionary games (EGs) with time-varying payoffs is studied by using the Lyapunov-based technique. First, the profile dynamics of EGs with time-varying payoffs is expressed into an algebraic form via the semi-tensor product of matrices. Second, a sufficient condition is obtained for the global stability of EGs with time-varying payoffs, and a common Lyapunov...
Using the semi-tensor product of matrices (STP), this paper investigates the Nash equilibrium and dynamics analysis of evolutionary networked games with multi-group. First, the formal evolutionary networked game model with multi-group is modeled as the multi-layer networked game. Second, based on the algebraic form of the utility function of each player, the necessary and sufficient condition for...
This paper investigates the algebraic formulation for a class of dynamic games with random entrance by using the semi-tensor product method, and presents a number of new results. The given dynamic game is considered as a kind of networked evolutionary games defined on finite networks, based on which, it is formulated as an Markov processes to analyze. Then, an illustrative example is studied to support...
The interaction neighborhood relationship among agents in many multi-agent systems is defined based on interaction radius r. Therefore, r plays an important role in the dynamics of these multi-agent systems. So does it also have influence on intervention methods for multi-agent systems? To answer this question, we study the impact of r on the performance of the Soft Control intervention method based...
We introduce a model of a cyclic game. Designed to take advantage of the recurring nature of certain economic and social situations, a cyclic game differs from an extensive form game in that a cyclic game does not necessarily have an end. The same situations, although with different players, may be repeated infinitely often. In this paper, the domain evolution process in a novel kind of cyclic game...
This paper is concerned with non-zero sum differential games of mean-field stochastic differential equations with partial information and convex control domain. First, applying the classical convex variations, we obtain stochastic maximum principle for Nash equilibrium points. Subsequently, under additional assumptions, verification theorem for Nash equilibrium points is also derived. Finally, as...
In this paper, a linear-quadratic leader-follower stochastic differential game with asymmetric information is studied. By maximum principle and stochastic filtering, a feedback Stackelberg equilibrium is given. The result can be regarded as a continuation of [5].
In this paper, we study the stochastic linear quadratic regulation problem for linear discrete-time systems with multiple input channels. A necessary and sufficient condition is obtained by applying the leader-follower game approach. Different from the augmentation technique, the complete solution is given in terms of one difference Riccati equation and one Riccati-type equation. The key is to introduce...
This paper studies social optima in the model of dynamic production competition by the mean field methodology. The objective of all agents (firms) is to optimize a social cost. We first introduce a market of a large number of firms with sticky prices and adjustment costs. The cost of each agent has indefinite state weights. By solving an auxiliary limiting optimal control problem subject to consistent...
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