In modeling the bilateral selection of states of the process, Dynkin (Dokl Akad Nauk USSR 185:241–288, 1969) proposed a two-person game in which players use stopping moments as strategies. The ...purpose of this work is to present a model of the game in which the players have different information about the process itself, as well as various laws to stop the process and accept its state. The game model uses the stochastic process apparatus, in particular, the ability to create different filters for the same process. The sets of stopping moments based on different filters are not identical, which allows us to model different sets of strategies for players. We show that the follower, by observing the behavior of a rational leader, can recover information that is lost due to the lack of complete observation of the state of the process. In the competition of two opponents for the maximum of the i.i.d. sequence, one of whom has access to full information and the other only knows their relative ranks, we found the generalized Stackelberg equilibrium. If the priority of a player observing the relative ranks is less than 50%, then that player modifies his strategy based on the behavior of the second player. For a player with full information, information about the behavior of the player observing the relative ranks is useless.
We will analyze the importance of elements of a complex structure on the availability of the system. The basis for the element assessment are the importance measures for multi-state systems ...introduced by Birnbaum (in: Krishaiah, Econometrics, principal components, reliability, and applications, Academic Press, New York, 1969) and Barlow and Proshan (Stoch Process Appl 3:153–173, 1975). The availability depends not only on the reliability, but also on the difficulty of maintenance, the ability to diagnose the need for service and its efficient implementation. If we assume that the need for maintenance is the result of deregulation, then determining the key elements to detect the moment of disorder of the system will be the basis for assessing the importance of the element for the system maintenance process.
Modeling the number of individuals in different states is a principal tool in the event of an epidemic. The natural transition of individuals between possible states often includes deliberate ...interference such as isolation or vaccination. Thus, the mathematical model may need to be re-calibrated due to various factors. The model considered in this paper is the SIRD epidemic model. An additional parameter is the moment of changing the description of the phenomenon when the parameters of the model change and the change is not pre-specified. Detecting and estimating the moment of change in real time is the subject of statistical research. A sequential (online) approach was applied using the Bayesian shift point detection algorithm and trimmed exact linear time. We show how methods of analysis behave in different instances. These methods are verified on simulated data and applied to pandemic data of a selected European country. The simulation is performed with a social network graph to obtain a practical representation ability. The epidemiological data used come from the territory of Poland and concern the COVID-19 epidemic in Poland. The results show satisfactory detection of the moments where the applied model needs to be verified and re-calibrated. These show the effectiveness of the proposed combination of methods.
The aim of the work is to connect individual behavior of drivers with traffic intensity. By diversifying the populations of drivers into two categories, often considered in this type of an analysis, ...CO (cooperative) and DE (defective), the tendency of drivers from each of these groups to deviate from compliance with traffic rules is established. The effective driver behavior translates into disrupting traffic by slowing it down. Participant interactions are described using game theories that provide information for simulations algorithms based on cellular automata. Three different ways of using this combination of descriptions of traffic participants to examine the impact of their behavior on the traffic dynamics are shown. Directions of the further, detailed analysis are indicated, which requires basic research in the field of game theory models.
The decision-maker (DM) sequentially evaluates up to N of different, rankable options. DM must select exactly the best one at the moment of its appearance. In the process of searching, DM finds out ...with each applicant whether she is the best applicant among those assessed so far (we call him a candidate). DM cannot return to rejected candidates. We discuss the psychological aspects of this selection problem, known in the literature as the secretary problem. The analysis is based on knowledge of the chances, and a subjective assessment of acceptance of the positive and negative effects DM’s decision. The acceptance assessment of success and failure is presented on subjective scales. We set an optimal policy that recommends analyzing applicants up to a certain point in time (a threshold time) without selecting any of them and then selecting the next encountered candidate. The determined optimal threshold depends on the level of acceptance of the positive and negative effects of the choice. This issue is discussed in the article.
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•Early candidates’ admission may be the unconscious inclusion of penalties.•An additional factor that regulates the selector’s behavior is the shortening of the time to complete the selection procedure.•Unavailable candidates greatly increase the chance and speed up finalize choice.•Controlling various risks increases the selector’s flexibility.
A milestone in the mathematical modeling of complex systems is the analysis of the significance of the system components. When examining the reliability, Birnbaum (1968) proposed measures of element ...significance. This direction of research into mathematical models of systems has led to many alternative analyzes. The aim of the article is to further expand the diagnostic capabilities of systems through a specialized analysis of their mathematical models. We propose, using the methods of game theory and stochastic processes, functionals that measure the structural reliability of the system and the operational performance related to maintenance. This allows for the construction of a new measure of significance, using knowledge of system design, reliability, and wear to optimize repair and maintenance. The considerations of this work are aimed at showing the ways of applying this approach to multi-state systems.
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