Displaying similar documents to “Maximum length of a series in a Markovian binary sequence with an application to the description of a basketball game”

Handling a Kullback-Leibler divergence random walk for scheduling effective patrol strategies in Stackelberg security games

César U. S. Solis, Julio B. Clempner, Alexander S. Poznyak (2019)

Kybernetika

Similarity:

This paper presents a new model for computing optimal randomized security policies in non-cooperative Stackelberg Security Games (SSGs) for multiple players. Our framework rests upon the extraproximal method and its extension to Markov chains, within which we explicitly compute the unique Stackelberg/Nash equilibrium of the game by employing the Lagrange method and introducing the Tikhonov regularization method. We also consider a game-theory realization of the problem that involves...

Some remarks on equilibria in semi-Markov games

Andrzej Nowak (2000)

Applicationes Mathematicae

Similarity:

This paper is a first study of correlated equilibria in nonzero-sum semi-Markov stochastic games. We consider the expected average payoff criterion under a strong ergodicity assumption on the transition structure of the games. The main result is an extension of the correlated equilibrium theorem proven for discounted (discrete-time) Markov games in our joint paper with Raghavan. We also provide an existence result for stationary Nash equilibria in the limiting average payoff semi-Markov...

Comparison of Sojourn Time Distributions in Modeling HIV/AIDS Disease Progression

Tilahun Ferede Asena, Ayele Taye Goshu (2017)

Biometrical Letters

Similarity:

An application of semi-Markov models to AIDS disease progression was utilized to find best sojourn time distributions. We obtained data on 370 HIV/AIDS patients who were under follow-up from September 2008 to August 2015, from Yirgalim General Hospital, Ethiopia. The study reveals that within the “good” states, the transition probability of moving from a given state to the next worst state has a parabolic pattern that increases with time until it reaches a maximum and then declines over...

Nonzero-sum semi-Markov games with countable state spaces

Wojciech Połowczuk (2000)

Applicationes Mathematicae

Similarity:

We consider nonzero-sum semi-Markov games with a countable state space and compact metric action spaces. We assume that the payoff, mean holding time and transition probability functions are continuous on the action spaces. The main results concern the existence of Nash equilibria for nonzero-sum discounted semi-Markov games and a class of ergodic semi-Markov games with the expected average payoff criterion.

Cumulative processes in basketball games

I. Kopocińska, B. Kopociński (2006)

Applicationes Mathematicae

Similarity:

We assume that the current score of a basketball game can be modeled by a bivariate cumulative process based on some marked renewal process. The basic element of a game is a cycle, which is concluded whenever a team scores. This paper deals with the joint probability distribution function of this cumulative process, the process describing the host's advantage and its expected value. The practical usefulness of the model is demonstrated by analyzing the effect of small modifications of...

Correlated equilibria in competitive staff selection problem

David M. Ramsey, Krzysztof Szajowski (2006)

Banach Center Publications

Similarity:

This paper deals with an extension of the concept of correlated strategies to Markov stopping games. The Nash equilibrium approach to solving nonzero-sum stopping games may give multiple solutions. An arbitrator can suggest to each player the decision to be applied at each stage based on a joint distribution over the players' decisions. This is a form of equilibrium selection. Examples of correlated equilibria in nonzero-sum games related to the staff selection competition in the case...

Bi-personal stochastic transient Markov games with stopping times and total reward criterion

Martínez-Cortés Victor Manuel (2021)

Kybernetika

Similarity:

The article is devoted to a class of Bi-personal (players 1 and 2), zero-sum Markov games evolving in discrete-time on Transient Markov reward chains. At each decision time the second player can stop the system by paying terminal reward to the first player. If the system is not stopped the first player selects a decision and two things will happen: The Markov chain reaches next state according to the known transition law, and the second player must pay a reward to the first player. The...

On distribution of waiting time for the first failure followed by a limited length success run

Czesław Stępniak (2013)

Applicationes Mathematicae

Similarity:

Many doctors believe that a patient will survive a heart attack unless a succeeding attack occurs in a week. Treating heart attacks as failures in Bernoulli trials we reduce the lifetime after a heart attack to the waiting time for the first failure followed by a success run shorter than a given k. In order to test the "true" critical period of the lifetime we need its distribution. The probability mass function and cumulative distribution function of the waiting time are expressed in...

Markov stopping games with an absorbing state and total reward criterion

Rolando Cavazos-Cadena, Luis Rodríguez-Gutiérrez, Dulce María Sánchez-Guillermo (2021)

Kybernetika

Similarity:

This work is concerned with discrete-time zero-sum games with Markov transitions on a denumerable space. At each decision time player II can stop the system paying a terminal reward to player I, or can let the system to continue its evolution. If the system is not halted, player I selects an action which affects the transitions and receives a running reward from player II. Assuming the existence of an absorbing state which is accessible from any other state, the performance of a pair...

Central limit theorem for hitting times of functionals of Markov jump processes

Christian Paroissin, Bernard Ycart (2004)

ESAIM: Probability and Statistics

Similarity:

A sample of i.i.d. continuous time Markov chains being defined, the sum over each component of a real function of the state is considered. For this functional, a central limit theorem for the first hitting time of a prescribed level is proved. The result extends the classical central limit theorem for order statistics. Various reliability models are presented as examples of applications.