Mathematical simulation of a dynamic game in the enterprise competition problem

Konstantinov, Roman Viktorovich; Половинкин, Е. С.

doi:10.1007/s10559-005-0009-8

Cited by 12 publications

(8 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The backward induction provides a simple solution: regardless of whether you have a better or a worse shot, the shooting moment when the sum of the success probabilities passes the threshold is the most critical [4]. On the other hand, this proposed game is a variant of a real-time based antagonistic stochastic game, and it adapts a duel game on top of conventional antagonistic stochastic games [5][6][7][8][9]. Each player at random times with random impacts can take the best shooting after passing the fixed threshold.…”

Section: Introductionmentioning

confidence: 99%

A Versatile Stochastic Duel Game

Kim

2020

Mathematics

View full text Add to dashboard Cite

This paper deals with a standard stochastic game model with a continuum of states under the duel-type setup. It newly proposes a hybrid model of game theory and the fluctuation process, which could be applied for various practical decision making situations. The unique theoretical stochastic game model is targeted to analyze a two-person duel-type game in the time domain. The parameters for strategic decisions including the moments of crossings, prior crossings, and the optimal number of iterations to get the highest winning chance are obtained by the compact closed joint functional. This paper also demonstrates the usage of a new time based stochastic game model by analyzing a conventional duel game model in the distance domain and briefly explains how to build strategies for an atypical business case to show how this theoretical model works.

show abstract

Section: Introductionmentioning

confidence: 99%

A Versatile Stochastic Duel Game

Kim

2020

Mathematics

View full text Add to dashboard Cite

show abstract

“…The literature on games is vast and a part of it is that on cooperative games, like [6], while other parts belong to the class of noncooperative (antagonistic) games. Noncooperative games [1,5,10] have also been widely used in economics [7] and some warfare [11]. The main technique we are using in this paper falls into the area of fluctuation analysis related to the random walk and occurring economics [2,8], physics [9], and other areas of engineering and technology.…”

Section: Introductionmentioning

confidence: 99%

Layers of noncooperative games

Dshalalow¹,

Ke²

2009

Nonlinear Analysis: Theory, Methods & Applications

View full text Add to dashboard Cite

“…They are also a part of differential games, most commonly applied to modeling and analysis of economics and management problems, which are characterized by both multiperiods and strategic decision making. An example is an antagonistic game model of the competition between two enterprises that manufacture the same homogeneous goods and operate on a given interval of time [56]. Other applications of differential games are nonlinear dynamics [13] and computer science [43].…”

Section: Introductionmentioning

confidence: 99%

Random Walk Analysis in Antagonistic Stochastic Games

Dshalalow

2008

Stochastic Analysis and Applications

View full text Add to dashboard Cite

This article deals with two "antagonistic random processes" that are intended to model classes of completely noncooperative games occurring in economics, engineering, natural sciences, and warfare. In terms of game theory, these processes can represent two players with opposite interests. The actions of the players are manifested by a series of strikes of random magnitudes imposed onto the opposite side and rendered at random times. Each of the assaults is aimed to inflict damage to vital areas. In contrast with some strictly antagonistic games where a game ends with one single successful hit, in the current setting, each side (player) can endure multiple strikes before perishing. Each player has a fixed cumulative threshold of tolerance which represents how much damage he can endure before succumbing. Each player will try to defeat the adversary at his earliest opportunity, and the time when one of them collapses is referred to as the "ruin time". We predict the ruin time of each player, and the cumulative status of all related components for each player at ruin time. The actions of each player are formalized by a marked point process representing (an economic) status of each opponent at any given moment of time. Their marks are assumed to be weakly monotone, which means that each opposite side accumulates damages, but does not have the ability to recover. We render a time-sensitive analysis of a bivariate continuous time parameter process representing the status of each player at any given time and at the ruin time and obtain explicit formulas for related functionals.

show abstract

Mathematical simulation of a dynamic game in the enterprise competition problem

Cited by 12 publications

References 3 publications

A Versatile Stochastic Duel Game

A Versatile Stochastic Duel Game

Layers of noncooperative games

Random Walk Analysis in Antagonistic Stochastic Games

Contact Info

Product

Resources

About