Nonzero-sum Stochastic Games

This paper treats of stochastic games. We focus on nonzero-sum games and provide a detailed survey of selected recent results. In Section 1, we consider stochastic Markov games. A correlation of strategies of the players, involving ``public signals'', is described, and a correlated equilibrium theorem proved recently by Nowak and Raghavan for discounted stochastic games with general state space is presented. We also report an extension of this result to a class of undiscounted stochastic games, satisfying some uniform ergodicity condition. Stopping games are related to stochastic Markov games. In Section 2, we describe a version of Dynkin's game related to observation of a Markov process with random assignment mechanism of states to the players. Some recent contributions of the second author in this area are reported. The paper also contains a brief overview of the theory of nonzero-sum stochastic games and stopping games which is very far from being complete.average payoff stochastic games, correlated stationary equilibria, nonzero-sum games, stopping time, stopping games

Persistently optimal policies in stochastic dynamic programming with generalized discounting

In this paper we study a Markov decision process with a non-linear discount function. Our approach is in spirit of the von Neumann-Morgenstern concept and is based on the notion of expectation. First, we define a utility on the space of trajectories of the process in the finite and infinite time horizon and then take their expected values. It turns out that the associated optimization problem leads to a non-stationary dynamic programming and an infinite system of Bellman equations, which result in obtaining persistently optimal policies. Our theory is enriched by examples.Stochastic dynamic programming, Persistently optimal policies, Variable discounting, Bellman equation, Resource extraction, Growth theory

On approximate and weak correlated equilibria in constrained discounted stochastic games

In this paper, we consider constrained discounted stochastic games with a countably generated state space and norm continuous transition probability having a density function. We prove existence of approximate stationary equilibria and stationary weak correlated equilibria. Our results imply the existence of stationary Nash equilibrium in $ARAT$ stochastic games

Effect of Edge-Stiffening and Diaphragms on the Reliability of Bridge Girders

Secondary elements such as barriers, sidewalks, and diaphragms may affect the distribution of live load to bridge girders. The objective of this study is to evaluate their effect on girder reliability if these elements are designed to be sufficiently attached to the bridge so as not to detach under traffic live loads. Simple span, two lane structures are considered, with composite steel girders supporting a reinforced concrete deck. Several representative structures are selected, with various configurations of barriers, sidewalks and diaphragms. Bridge analysis is performed using a finite element procedure. Load and resistance parameters are treated as random variables. Random variables considered are composite girder flexural strength, secondary element stiffness, load magnitude (dead load and truck traffic live load), and live load position. It was found that typical combinations of secondary elements have a varying influence on girder reliability, depending on secondary element stiffness and bridge geometry. Suggestions are presented that can account for secondary elements and that provide a uniform level of reliability to bridge girders

Reliability Analysis of Plank Decks

The objective of this study is to summarize the load and resistance criteria for highway bridge plank decks, and to estimate the reliability of plank decks designed by AASHTO Code. Both transverse and longitudinal planks for a variety of typical stringer spacings and plank sizes are considered. Truck traffic load data is based on the model used to calibrate the 1994 AASHTO LRFD Code. However, for plank decks, wheel load rather than whole vehicle weight is most important, and these statistics are developed for this study. For wood planks, dead load and dynamic load are not significant. The limit state considered is flexural strength, and resistance statistics are presented for wood planks in terms of modulus of rupture. Special flat-wise use data are presented to account for section aspect ratio as well as edge of load application. The reliability analysis is carried out using the procedure developed for calibration of AASHTO LRFD. Reliability indices for both AASHTO Standard and AASHTO LRFD Code are presented for plank decks. The results indicate that there are considerable differences in plank reliability indices. Causes of inconsistencies in safety are identified