A Class of Mean-field LQG Games with Partial Information

The large-population system consists of considerable small agents whose individual behavior and mass effect are interrelated via their state-average. The mean-field game provides an efficient way to get the decentralized strategies of large-population system when studying its dynamic optimizations. Unlike other large-population literature, this current paper possesses the following distinctive features. First, our setting includes the partial information structure of large-population system which is practical from real application standpoint. Specially, two cases of partial information structure are considered here: the partial filtration case (see Section 2, 3) where the available information to agents is the filtration generated by an observable component of underlying Brownian motion; the noisy observation case (Section 4) where the individual agent can access an additive white-noise observation on its own state. Also, it is new in filtering modeling that our sensor function may depend on the state-average. Second, in both cases, the limiting state-averages become random and the filtering equations to individual state should be formalized to get the decentralized strategies. Moreover, it is also new that the limit average of state filters should be analyzed here. This makes our analysis very different to the full information arguments of large-population system. Third, the consistency conditions are equivalent to the wellposedness of some Riccati equations, and do not involve the fixed-point analysis as in other mean-field games. The $\epsilon$-Nash equilibrium properties are also presented.Comment: 19 page

Mean Field Linear-Quadratic-Gaussian (LQG) Games of Forward-Backward Stochastic Differential Equations

This paper studies a new class of dynamic optimization problems of large-population (LP) system which consists of a large number of negligible and coupled agents. The most significant feature in our setup is the dynamics of individual agents follow the forward-backward stochastic differential equations (FBSDEs) in which the forward and backward states are coupled at the terminal time. This current paper is hence different to most existing large-population literature where the individual states are typically modeled by the SDEs including the forward state only. The associated mean-field linear-quadratic-Gaussian (LQG) game, in its forward-backward sense, is also formulated to seek the decentralized strategies. Unlike the forward case, the consistency conditions of our forward-backward mean-field games involve six Riccati and force rate equations. Moreover, their initial and terminal conditions are mixed thus some special decoupling technique is applied here. We also verify the $\epsilon$-Nash equilibrium property of the derived decentralized strategies. To this end, some estimates to backward stochastic system are employed. In addition, due to the adaptiveness requirement to forward-backward system, our arguments here are not parallel to those in its forward case.Comment: 21 page

A Unified Relation Analysis of Linear-quadratic Mean-field Game, Team and Control

This paper revisits well-studied dynamic decisions of weakly coupled large-population (LP) systems. Specifically, three types of LP decision problems: mean-field game (MG), mean-field team (MT), and mean-field-type control (MC), are completely analyzed in a general stochastic linear-quadratic setting with controlled-diffusion in state dynamics and indefinite weight in cost functional. More importantly, interrelations among MG, MT and MC are systematically discussed; some relevant interesting findings are reported that may be applied to a structural analysis of general LP decisions

Linear quadratic mean-field game-team analysis: a mixed coalition approach

Mean-field theory has been extensively explored in decision analysis of {large-scale} (LS) systems but traditionally in ``pure" cooperative or competitive settings. This leads to the so-called mean-field game (MG) or mean-field team (MT). This paper introduces a new class of LS systems with cooperative inner layer and competitive outer layer, so a ``mixed" mean-field analysis is proposed for distributed game-team strategy. A novel asymptotic mixed-equilibrium-optima is also proposed and verified

The Berardenga Antependium and the Passio Ymaginis Office

Table S1. Signatures summary. A summary of 33 signatures about the platforms derived from, the subtypes used for, the gene number included, and the function terms involved. Table S8. The number of function terms in each signature. (PDF 82 kb

The research of 3D small-field imaging system based on fringe projection technique

This paper presents a 3D small-field imaging system by using the color fringe projection technique to measure the small objects having large slopes and/or discontinuous surface. A stereo microscope is used to generate a small-field projecting field and to capture the deformed fringe patterns on the measured small objects, respectively. Three fringe sets having the optimum fringe numbers are coded into one major color channel to generate color fringe patterns having the maximum fringe contrast of the captured fringe images. Through one channel of the stereo microscope, a DLP (Digital Light Processing) projector projects these generated color fringe pattern images onto the measured objects surface. From another channel, the fringe patterns are deformed with regard to the object surface and captured by a color CCD camera. The absolute phase of each pixel can be calculated from the captured fringe patterns by using the optimum three-fringe numbers selection method. Experimental results on measuring 3D shape of small objects show the accuracy and availability of the developed 3D imaging system

Projector calibration method based on optical coaxial camera

This paper presents a novel method to accurately calibrate a DLP projector by using an optical coaxial camera to capture the needed images. A plate beam splitter is used to make imaging axis of the CCD camera and projecting axis of the DLP projector coaxial, so the DLP projector can be treated as a true inverse camera. A plate having discrete markers on the surface will be designed and manufactured to calibrate the DLP projector. By projecting vertical and horizontal sinusoidal fringe patterns on the plate surface from the projector, the absolute phase of each marker’s center can be obtained. The corresponding projector pixel coordinate of each marker is determined from the obtained absolute phase. The internal and external parameters of the DLP projector are calibrated by the corresponding point pair between the projector coordinate and the world coordinate of discrete markers. Experimental results show that the proposed method accurately obtains the parameters of the DLP projector. One advantage of the method is the calibrated internal and external parameters have high accuracy because of uncalibrating the camera. The other is the optical coaxes geometry gives a true inverse camera, so the calibrated parameters are more accurate than that of crossed-optical-axes, especially the principal points and the radial distortion coefficients of the projector lens