Model and Reinforcement Learning for Markov Games with Risk Preferences

We motivate and propose a new model for non-cooperative Markov game which considers the interactions of risk-aware players. This model characterizes the time-consistent dynamic "risk" from both stochastic state transitions (inherent to the game) and randomized mixed strategies (due to all other players). An appropriate risk-aware equilibrium concept is proposed and the existence of such equilibria is demonstrated in stationary strategies by an application of Kakutani's fixed point theorem. We further propose a simulation-based Q-learning type algorithm for risk-aware equilibrium computation. This algorithm works with a special form of minimax risk measures which can naturally be written as saddle-point stochastic optimization problems, and covers many widely investigated risk measures. Finally, the almost sure convergence of this simulation-based algorithm to an equilibrium is demonstrated under some mild conditions. Our numerical experiments on a two player queuing game validate the properties of our model and algorithm, and demonstrate their worth and applicability in real life competitive decision-making.Comment: 38 pages, 6 tables, 5 figure

Multi-valued weighted composition operators on Fock space

Multivalued linear operators, also known as linear relations, are studied on a specific class of weighted, composition transforms on Fock space. Basic properties of this class of linear relations, such as closed graph, boundedness, complex symmetry, real symmetry, or isometry are characterized in simple algebraic terms, involving their symbols

THE UNIFORM EXPONENTIAL STABILITY OF LINEAR SKEW-PRODUCT SEMIFLOWS ON REAL HILBERT SPACE

The goal of the paper is to present some characterizations for the uniform exponential stability of linear skew-product semiflows on real Hilbert space

Bacteria associated with soft coral from Mot island - Nha Trang bay and their antimicrobial activities

Microbial communities associated with invertebrates had been considered as a new source of bioactive compounds. The soft coral associated bacteria in Mot island, Nha Trang bay were isolated, extracted and assessed for antagonistic activity against human and coral pathogens, the strongly active strains were identified by 16S rRNA analysis. The soft coral associated bacterium SCN10 had abcd antibacterial pattern which was named for inhibition towards Bacillus subtilis (pattern a), Escherichia coli (pattern b), Salmonella typhimurium (pattern c) and Serratia marcescens (pattern d). It was the nearest strain to the well-known antibiotic producer Bacillus amyloliquefaciens with 99% sequence similarity. Whereas strain SCL19 had abde pattern which means inhibition of the growth of B. subtilis, E. coli, S. marcescens and Vibrio parahaemolyticus (pattern e). This strain SCL19 affiliated with Bacillus sp. strain A-3-23B with 99.8% identity. In addition to antimicrobial activity to the aforementioned tested bacteria, the isolate SCX15 also inhibited Vibrio alginolyticus (pattern f) and Candida albicans (pattern g), so this isolate possessed abcdefg antimicrobial pattern. The coral associated isolate SCX15 was identified as Bacillus velezensis with 99% sequence similarity. Among the 78 screened strains, 25 isolates possessed antibacterial activity against at least one of seven tested microorganisms and exhibited 12 different types of antimicrobial activities, suggesting that they can produce many different natural substances with antibacterial activity