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We show that right-continuous monotone strategies used in Markov perfect equilibria for economic growth models and related dynamic games can be recognised as members of the Hilbert space of square integrable functions of the state variable. We provide an application of this result to a bequest game and point out that this result also holds for the class of left-continuous monotone functions. The result is fundamental for using the Schauder fixed point theorem. Furthermore, it considerably simplifies the classical approach, where such strategies are represented by non-negative measures on the state space.

In this paper, we study a Markov decision process with a non-linear discount function and with a Borel state space. We define a recursive discounted utility, which resembles non-additive utility functions considered in a number of models in economics. Non-additivity here follows from non-linearity of the discount function. Our study is complementary to the work of Jaśkiewicz et al. (Math Oper Res 38:108–121, 2013), where also non-linear discounting is used in the stochastic setting, but the expectation of utilities aggregated on the space of all histories of the process is applied leading to a non-stationary dynamic programming model. Our aim is to prove that in the recursive discounted utility case the Bellman equation has a solution and there exists an optimal stationary policy for the problem in the infinite time horizon. Our approach includes two cases: (a) when the one-stage utility is bounded on both sides by a weight function multiplied by some positive and negative constants, and (b) when the one-stage utility is unbounded from below.

We study Markov decision processes with Borel state spaces under quasi-hyperbolic discounting. This type of discounting nicely models human behaviour, which is time-inconsistent in the long run. The decision maker has preferences changing in time. Therefore, the standard approach based on the Bellman optimality principle fails. Within a dynamic game-theoretic framework, we prove the existence of randomised stationary Markov perfect equilibria for a large class of Markov decision processes with transitions having a density function. We also show that randomisation can be restricted to two actions in every state of the process. Moreover, we prove that under some conditions, this equilibrium can be replaced by a deterministic one. For models with countable state spaces, we establish the existence of deterministic Markov perfect equilibria. Many examples are given to illustrate our results, including a portfolio selection model with quasi-hyperbolic discounting.

There has been a considerable progress in the reliability-based code development procedures. The load and resistance factors in the AASHTO bridge design code were determined using the statistical parameters from the 1970's and early 1980’s. Load and resistance factors were determined by first fixing the load factors and then calculating resistance factors. Load factors were selected so that the factored load corresponds to two standard deviations from the mean value and the resistance factors were calculated so that the reliability index is close to the target value. However, from the theoretical point of view, the load and resistance factors are to be determined as coordinates of the so-called “design point” that corresponds to less than two standard deviations from the mean. Therefore, the optimum load and resistance factors are about 10% lower than what is in the AASHTO LRFD Code. The objective of this paper is to revisit the original calibration and recalculate the load and resistance factors as coordinates of the “design point” for prestressed concrete girder bridges. The recommended new load and resistance factors provide a consistent reliability and a rational safety margin.

As a matter of fact, structural drift is a random variable that is associated with several bases of the uncertainties related to the loading excitation and structural resistance. Hence, it seems es...

Weigh-in-motion (WIM) data provide an excellent opportunity to study the effects of actual traffic loads on bridges. Here procedures are presented for using WIM data to quantify the fatigue damage accumulated in steel bridges. These procedures allow comparisons of the impacts of truck traffic on various routes beyond simple comparisons of the numbers and gross vehicles weights of trucks in the traffic streams. The fatigue damage accumulation procedures are demonstrated using WIM traffic data collected in the state of Alabama. The results of the analysis show that approximately 20% of trucks are overloaded, that is, permit loads and illegal loads, and those trucks create more than 50% of the total damage based on the combined data from all the WIM locations in the state. The contribution of overloaded trucks to the total fatigue damage varies so that their contribution is less significant along some routes. A typical steel bridge with bottom flange coverplates was evaluated using the WIM data from 1 year for a heavily traveled route. This analysis shows that the fatigue life of the bridge was consumed at an annual rate consistent with a mean life of 100 years. These procedures have applications in planning weight limit enforcement, budgeting, and maintenance, and they have the potential for future use in planning inspection intervals.

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.

This study aims to develop Load and Resistance Factor Design (LRFD) provisions for movable bridges’ mechanical components. It requires the formulation of the limit state functions, determi...