Bayesian Nash equilibrium seeking for multi-agent incomplete-information aggregative games

summary:In this paper, we consider a distributed Bayesian Nash equilibrium (BNE) seeking problem in incomplete-information aggregative games, which is a generalization of either Bayesian games or deterministic aggregative games. We handle the aggregation function to adapt to incomplete-information situations. Since the feasible strategies are infinite-dimensional functions and lie in a non-compact set, the continuity of types brings barriers to seeking equilibria. To this end, we discretize the continuous types and then prove that the equilibrium of the derived discretized model is an $\epsilon$-BNE. On this basis, we propose a distributed algorithm for an $\epsilon$-BNE and further prove its convergence

Bayesian Nash Equilibrium Seeking for Distributed Incomplete-information Aggregative Games

In this paper, we consider a distributed Bayesian Nash equilibrium (BNE) seeking problem in incomplete-information aggregative games, which is a generalization of Bayesian games and deterministic aggregative games. We handle the aggregation function for distributed incomplete-information situations. Since the feasible strategies are infinite-dimensional functions and lie in a non-compact set, the continuity of types brings barriers to seeking equilibria. To this end, we discretize the continuous types and then prove that the equilibrium of the derived discretized model is an $\epsilon$-BNE. On this basis, we propose a distributed algorithm for an $\epsilon$-BNE and further prove its convergence

Distributed Algorithm for Continuous-type Bayesian Nash Equilibrium in Subnetwork Zero-sum Games

In this paper, we consider a continuous-type Bayesian Nash equilibrium (BNE) seeking problem in subnetwork zero-sum games, which is a generalization of deterministic subnetwork zero-sum games and discrete-type Bayesian zero-sum games. In this continuous-type model, because the feasible strategy set is composed of infinite-dimensional functions and is not compact, it is hard to seek a BNE in a non-compact set and convey such complex strategies in network communication. To this end, we design two steps to overcome the above bottleneck. One is a discretization step, where we discretize continuous types and prove that the BNE of the discretized model is an approximate BNE of the continuous model with an explicit error bound. The other one is a communication step, where we adopt a novel compression scheme with a designed sparsification rule and prove that agents can obtain unbiased estimations through compressed communication. Based on the above two steps, we propose a distributed communication-efficient algorithm to practicably seek an approximate BNE, and further provide an explicit error bound and an $O(\ln T/\sqrt{T})$ convergence rate.Comment: Submitted to SIAM Journal on Control and Optimizatio

Stabilized antiferroelectricity in xBiScO3-(1-x)NaNbO3 lead-free ceramics with established double hysteresis loops

We previously reported various solid solution systems that demonstrated the stabilized antiferroelectric (P) phases in NaNbO 3 through lowering the tolerance factor. However, all those reported modifications were achieved by adding A 2+ B 4+ O 3 type solid solutions. A lead-free antiferroelectric (AFE) solid solution xBiScO 3 -(1-x)NaNbO 3 was rationalized by adopting the tolerance factor design rule. Specifically, adding BiScO 3 was found to effectively stabilize the AFE phase without changing the crystal symmetry of NaNbO 3 . Microstructure and electron zone axis diffraction patterns from transmission electron microscopy revealed the stabilized AFE (P) phase in this solid solution. Besides, the electric-field-induced polarization with a double-hysteresis loop was observed. The present results pointed out that the strategy could also be applied while adding A 3+ B 3+ O 3 type solid solutions. In addition, it expanded the compositional design that can be applied to antiferroelectric materials

Microstructural origin for the piezoelectricity evolution in (K0.5Na0.5)NbO3-based lead-free ceramics

Chemically modified (K0.5Na0.5)NbO3 compositions with finely tuned polymorphic phase boundaries (PPBs) have shown excellent piezoelectric properties. The evolution of the domain morphology and crystal structure under applied electric fields of a model material, 0.948(K0.5Na0.5)NbO3-0.052LiSbO3, was directly visualized using in situ transmission electron microscopy. The in situ observations correlate extremely well with measurements of the electromechanical response on bulk samples. It is found that the origin of the excellent piezoelectric performance in this lead-free composition is due to a tilted monoclinic phase that emerges from the PPB when poling fields greater than 14 kV/cm are applied. 2013 AIP Publishing LLC

Temporal variations of the two oxygen depleted zones in the Bohai Sea

The Bohai Sea (BS) has been experiencing prominent deoxygenation in recent years that forms a typically coastal oxygen depleted region in summer. A three-dimensional coupled physical-biogeochemical model was used in this study to investigate temporal variations of the two separately-developing oxygen depleted zones in the BS. Comparison with observations shows a good model performance for multi-year’s oxygen depletion simulation. Two separately-developing oxygen depleted cores are always identified in these years with a threshold of oxygen concentration less than 3 mg/L. The oxygen depletion in the northern core is generally more severe with larger areas and lower oxygen minima. During the evolution of oxygen depletion, the bottom oxygen concentration decreases more smoothly in the northern core, while fluctuates frequently in the southern core. Nonetheless, the oxygen depletion in both cores fades away almost simultaneously, with a sudden oxygen increase in late summer or early autumn. Oxygen budget estimation indicates that the biological oxygen consumption in the southern core is greater than that in the northern core, but compensated by the oxygen replenishment of oxygen-rich water from the Bohai Strait and vertical diffusion of the water column, which is less in the northern core, so that the oxygen depletion in the northern core is more severe. During oxygen depletion development in June and July, bottom oxygen in the southern core is more susceptible to strong winds than the northern core attributed to differences in topography, with a shallower and smoother bathymetry leading to weaker water column stability in summer. Recognition of characteristics of the two separate oxygen depleted cores would advance understanding spatial pattern of oxygen dynamics and provide a basis for statistical seasonal prediction of coastal oxygen depletion with consideration of spatial heterogeneity

Base Metal Co-Fired Multilayer Piezoelectrics

Piezoelectrics have been widely used in different kinds of applications, from the automobile industry to consumer electronics. The novel multilayer piezoelectrics, which are inspired by multilayer ceramic capacitors, not only minimize the size of the functional parts, but also maximize energy efficiency. Development of multilayer piezoelectric devices is at a significant crossroads on the way to achieving low costs, high efficiency, and excellent reliability. Concerning the costs of manufacturing multilayer piezoelectrics, the trend is to replace the costly noble metal internal electrodes with base metal materials. This paper discusses the materials development of metal co-firing and the progress of integrating current base metal chemistries. There are some significant considerations in metal co-firing multilayer piezoelectrics: retaining stoichiometry with volatile Pb and alkaline elements in ceramics, the selection of appropriate sintering agents to lower the sintering temperature with minimum impact on piezoelectric performance, and designing effective binder formulation for low pO2 burnout to prevent oxidation of Ni and Cu base metal

MULTI-SCALE ANALYSIS OF CRYOGENIC COMPOSITE STRUCTURES CONSIDERING INTERFACIAL PHASE

Fiber/matrix interfaces exist in the transitional region between fiber and resin matrix in fiber reinforced composites. How to reasonably consider the interposition of interfacial phase is a critical problem in the failure analysis of composite structures. In this paper, a multi-scale finite element method is proposed based on three-phase representative volume element, by developing the microscopic failure criterion, damage degradation model and uncertainty model of material strength. The failure prediction of low temperature composite structure under thermal mechanical load is realized by the multi-scale finite element method. Moreover, the method is used to analyze the failure of composite laminates at five temperatures. The numerical predictions are in good agreement with the experimental results, which shows that the method can analyze the failure of composite structures at cryogenic temperatures effectively