Stochastic Approach for Determining Stable Coalition Structure

2015 ◽  
Vol 17 (04) ◽  
pp. 1550009 ◽  
Author(s):  
Elena Parilina ◽  
Artem Sedakov
Keyword(s):  
Markov Chain ◽  
Nash Equilibrium ◽  
Special Form ◽  
Stochastic Game ◽  
Coalition Structure ◽  
Stochastic Approach ◽  
Tu Games ◽  
Absorbing State ◽  
Stable Coalition ◽  
Definition Of

In this paper, we study TU-games with coalition structure and propose an approach for determining a stable coalition structure solving a stochastic game of a special form. Using a Nash equilibrium in this game, we draw an analogy between the stable coalition structure and an absorbing state in a Markov chain. In addition, we consider a case of restricted coalitions assuming that not all coalitions are feasible and extend the definition of the stable coalition structure to this case.

scholarly journals Nash Equilibrium Sequence in a Singular Two-Person Linear-Quadratic Differential Game

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 132
Author(s):  
Valery Y. Glizer
Keyword(s):  
Nash Equilibrium ◽  
Differential Game ◽  
Quadratic Functional ◽  
Linear Quadratic ◽  
Feedback Controls ◽  
Cheap Control ◽  
Optimal Values ◽  
Definition Of ◽  
Zero Sum ◽  
Equilibrium Sequence

A finite-horizon two-person non-zero-sum differential game is considered. The dynamics of the game is linear. Each of the players has a quadratic functional on its own disposal, which should be minimized. The case where weight matrices in control costs of one player are singular in both functionals is studied. Hence, the game under the consideration is singular. A novel definition of the Nash equilibrium in this game (a Nash equilibrium sequence) is proposed. The game is solved by application of the regularization method. This method yields a new differential game, which is a regular Nash equilibrium game. Moreover, the new game is a partial cheap control game. An asymptotic analysis of this game is carried out. Based on this analysis, the Nash equilibrium sequence of the pairs of the players’ state-feedback controls in the singular game is constructed. The expressions for the optimal values of the functionals in the singular game are obtained. Illustrative examples are presented.

scholarly journals Proportional lumpability and proportional bisimilarity

2021 ◽  
Author(s):  
Andrea Marin ◽  
Carla Piazza ◽  
Sabina Rossi
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Upper And Lower Bounds ◽  
General Definition ◽  
Performance Indices ◽  
State Aggregation ◽  
Structural Regularity ◽  
Original Definition ◽  
Aggregation Technique ◽  
Definition Of

AbstractIn this paper, we deal with the lumpability approach to cope with the state space explosion problem inherent to the computation of the stationary performance indices of large stochastic models. The lumpability method is based on a state aggregation technique and applies to Markov chains exhibiting some structural regularity. Moreover, it allows one to efficiently compute the exact values of the stationary performance indices when the model is actually lumpable. The notion of quasi-lumpability is based on the idea that a Markov chain can be altered by relatively small perturbations of the transition rates in such a way that the new resulting Markov chain is lumpable. In this case, only upper and lower bounds on the performance indices can be derived. Here, we introduce a novel notion of quasi-lumpability, named proportional lumpability, which extends the original definition of lumpability but, differently from the general definition of quasi-lumpability, it allows one to derive exact stationary performance indices for the original process. We then introduce the notion of proportional bisimilarity for the terms of the performance process algebra PEPA. Proportional bisimilarity induces a proportional lumpability on the underlying continuous-time Markov chains. Finally, we prove some compositionality results and show the applicability of our theory through examples.

On the age distribution of a Markov chain

1978 ◽  
Vol 15 (1) ◽  
pp. 65-77 ◽  
Author(s):  
Anthony G. Pakes
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Limit Theorems ◽  
Age Distribution ◽  
Weak Limit ◽  
Absorbing State ◽  
Absorbing Markov Chain ◽  
Continuous Random Walk ◽  
A Chain ◽  
Watson Process

This paper develops the notion of the limiting age of an absorbing Markov chain, conditional on the present state. Chains with a single absorbing state {0} are considered and with such a chain can be associated a return chain, obtained by restarting the original chain at a fixed state after each absorption. The limiting age, A(j), is the weak limit of the time given Xn = j (n → ∞).A criterion for the existence of this limit is given and this is shown to be fulfilled in the case of the return chains constructed from the Galton–Watson process and the left-continuous random walk. Limit theorems for A (J) (J → ∞) are given for these examples.

UNCERTAINTY BASED ROBUST OPTIMIZATION IN AERODYNAMICS

2009 ◽  
Vol 23 (03) ◽  
pp. 477-480 ◽  
Author(s):  
ZHILI TANG
Keyword(s):  
Nash Equilibrium ◽  
Robust Design ◽  
Single Point ◽  
Optimization Method ◽  
Equilibrium Solutions ◽  
Design Problems ◽  
Nash Equilibrium Solutions ◽  
Definition Of ◽  
Taguchi Robust Design ◽  
Statistical Definition

The Taguchi robust design concept is combined with the multi-objective deterministic optimization method to overcome single point design problems in Aerodynamics. Starting from a statistical definition of stability, the method finds, Nash equilibrium solutions for performance and its stability simultaneously.

On the age distribution of a Markov chain

1978 ◽  
Vol 15 (01) ◽  
pp. 65-77 ◽  
Author(s):  
Anthony G. Pakes
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Limit Theorems ◽  
Age Distribution ◽  
Weak Limit ◽  
Absorbing State ◽  
Absorbing Markov Chain ◽  
Continuous Random Walk ◽  
A Chain ◽  
Watson Process

This paper develops the notion of the limiting age of an absorbing Markov chain, conditional on the present state. Chains with a single absorbing state {0} are considered and with such a chain can be associated a return chain,obtained by restarting the original chain at a fixed state after each absorption. The limiting age,A(j), is the weak limit of the timegivenXn=j(n → ∞).A criterion for the existence of this limit is given and this is shown to be fulfilled in the case of the return chains constructed from the Galton–Watson process and the left-continuous random walk. Limit theorems forA(J) (J →∞) are given for these examples.

scholarly journals Will this search end up with booking? Modeling airline booking conversion of anonymous visitors

2020 ◽  
Vol 27 (2) ◽  
pp. 237-250
Author(s):  
Misuk Lee
Keyword(s):  
Markov Chain ◽  
Transition Probabilities ◽  
Markov Chain Model ◽  
Distribution Channel ◽  
Stochastic Approach ◽  
Tourism Industry ◽  
Chain Model ◽  
Online Search ◽  
Clickstream Data ◽  
Content Type

Purpose Over the past two decades, online booking has become a predominant distribution channel of tourism products. As online sales have become more important, understanding booking conversion behavior remains a critical topic in the tourism industry. The purpose of this study is to model airline search and booking activities of anonymous visitors. Design/methodology/approach This study proposes a stochastic approach to explicitly model dynamics of airline customers’ search, revisit and booking activities. A Markov chain model simultaneously captures transition probabilities and the timing of search, revisit and booking decisions. The suggested model is demonstrated on clickstream data from an airline booking website. Findings Empirical results show that low prices (captured as discount rates) lead to not only booking propensities but also overall stickiness to a website, increasing search and revisit probabilities. From the decision timing of search and revisit activities, the author observes customers’ learning effect on browsing time and heterogeneous intentions of website visits. Originality/value This study presents both theoretical and managerial implications of online search and booking behavior for airline and tourism marketing. The dynamic Markov chain model provides a systematic framework to predict online search, revisit and booking conversion and the time of the online activities.

scholarly journals An Algorithmic Procedure for Finding Nash Equilibrium

2020 ◽  
Vol 40 (1) ◽  
pp. 71-85
Author(s):  
HK Das ◽  
T Saha
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Payoff Matrix ◽  
Matrix Game ◽  
Perfect Equilibrium ◽  
Repeated Use ◽  
Definition Of ◽  
Zero Sum ◽  
Mathematical Construction ◽  
Algorithmic Procedure

This paper proposes a heuristic algorithm for the computation of Nash equilibrium of a bi-matrix game, which extends the idea of a single payoff matrix of two-person zero-sum game problems. As for auxiliary but making the comparison, we also introduce here the well-known definition of Nash equilibrium and a mathematical construction via a set-valued map for finding the Nash equilibrium and illustrates them. An important feature of our algorithm is that it finds a perfect equilibrium when at the start of all actions are played. Furthermore, we can find all Nash equilibria of repeated use of this algorithm. It is found from our illustrative examples and extensive experiment on the current phenomenon that some games have a single Nash equilibrium, some possess no Nash equilibrium, and others had many Nash equilibria. These suggest that our proposed algorithm is capable of solving all types of problems. Finally, we explore the economic behaviour of game theory and its social implications to draw a conclusion stating the privilege of our algorithm. GANIT J. Bangladesh Math. Soc.Vol. 40 (2020) 71-85

scholarly journals A Stochastic Approach Towards Travel Route Optimization and Recommendation Based on Users Constraints Using Markov Chain

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 90760-90776 ◽  
Author(s):  
Shabir Ahmad ◽  
Israr Ullah ◽  
Faisal Mehmood ◽  
Muhammad Fayaz ◽  
DoHyeun Kim
Keyword(s):  
Markov Chain ◽  
Stochastic Approach ◽  
Route Optimization ◽  
Travel Route Optimization
Sign in / Sign up

Export Citation Format

Share Document