Jerzy Filar

Bilinear programming and structured stochastic games

Publisher: Springer Science and Business Media LLC

Date: 04-1987

DOI: 10.1007/BF00938818

Geometric interpretation of Hamiltonian cycles problem via singularly perturbed Markov decision processes

Publisher: Informa UK Limited

Date: 08-2003

DOI: 10.1080/02331930310001611529

Markov chains, Hamiltonian cycles and volumes of convex bodies

Publisher: Springer Science and Business Media LLC

Date: 23-11-2013

DOI: 10.1007/S10898-011-9819-6

A Linearly-Growing Conversion from the Set Splitting Problem to the Directed Hamiltonian Cycle Problem

Publisher: Springer Netherlands

Date: 2014

DOI: 10.1007/978-94-017-8044-5_3

An asymptotic simplex method for singularly perturbed linear programs

Publisher: Elsevier BV

Date: 10-2002

DOI: 10.1016/S0167-6377(02)00152-9

On the computation of equilibria in discounted stochastic dynamic games

Publisher: Elsevier BV

Date: 06-1986

DOI: 10.1016/0165-1889(86)90013-8

Constraint augmentation in pseudo-singularly perturbed linear programs

Publisher: Springer Science and Business Media LLC

Date: 16-06-2012

DOI: 10.1007/S10107-010-0388-0

On regularly perturbed fundamental matrices

Publisher: Elsevier BV

Date: 12-2007

DOI: 10.1016/J.JMAA.2007.01.107

ALGORITHM FOR SOLVING S-GAMES AND DIFFERENTIAL S-GAMES.

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Date: 11-1982

DOI: 10.1137/0320055

Foreword

Publisher: Springer Science and Business Media LLC

Date: 12-2018

DOI: 10.1007/S10666-018-9645-Z

The traveling inspector model

Publisher: Springer Science and Business Media LLC

Date: 03-1986

DOI: 10.1007/BF01720770

Time consistent dynamic risk measures

Publisher: Springer Science and Business Media LLC

Date: 26-01-2006

DOI: 10.1007/S00186-005-0045-1

Comparative forecasting and a test for persistence in the EL Ni ño Southern Oscillation

Publisher: Springer US

Date: 2010

DOI: 10.1007/978-1-4419-1129-2_9

The completely mixed single-controller stochastic game

Publisher: American Mathematical Society (AMS)

Date: 1985

DOI: 10.1090/S0002-9939-1985-0810169-4

Abstract: We consider a zero-sum stochastic game with finitely many states and actions. Further we assume that the transition probabilities depend on the actions of only one player (player II, in our case), and that the game is completely mixed . That is, every optimal stationary strategy for either player assigns a positive probability to every action in every state. For these games, properties analogous to those derived by Kaplansky [ 4 ] for the completely mixed matrix games, are established in this paper. These properties lead to the counterintuitive conclusion that the controller need not know the law of motion in order to play optimally, but his opponent does not have this luxury.

Hamiltonian cycles and singularly perturbed Markov chains

Publisher: Institute for Operations Research and the Management Sciences (INFORMS)

Date: 02-2004

DOI: 10.1287/MOOR.1030.0066

Abstract: We consider the Hamiltonian cycle problem embedded in a singularly perturbed Markov decision process. We also consider a functional on the space of deterministic policies of the process that consists of the (1,1)-entry of the fundamental matrices of the Markov chains induced by the same policies. We show that when the perturbation parameter, ε, is less than or equal to 1/N 2 , the Hamiltonian cycles of the directed graph are precisely the minimizers of our functional over the space of deterministic policies. In the process, we derive analytical expressions for the possible N distinct values of the functional over the, typically, much larger space of deterministic policies.

Risk sensitivity in Beverton–Holt fishery with multiplicative harvest

Publisher: Wiley

Date: 24-01-2020

DOI: 10.1111/NRM.12257

Some comments on a theorem of Hardy and Littlewood

Publisher: Springer Science and Business Media LLC

Date: 10-1992

DOI: 10.1007/BF00939913

Stochastic Target Hitting Time and the Problem of Early Retirement

Publisher: Institute of Electrical and Electronics Engineers (IEEE)

Date: 03-2004

DOI: 10.1109/TAC.2004.824469

Australian electricity market and price volatility

Publisher: Springer Science and Business Media LLC

Date: 10-12-2016

DOI: 10.1007/S10479-011-1033-X

Quadratic programming and the single-controller stochastic game

Publisher: Elsevier BV

Date: 1986

DOI: 10.1016/0022-247X(86)90338-0

Solving the Hamiltonian Cycle problem using symbolic determinants

Publisher: The Mathematical Society of the Republic of China

Date: 02-2006

DOI: 10.11650/TWJM/1500403828

Determinants and longest cycles of graphs

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Date: 2008

DOI: 10.1137/070693898

Weighted singularly perturbed hybrid stochastic systems

Publisher: Springer Science and Business Media LLC

Date: 09-2005

DOI: 10.1007/S00186-005-0440-7

On stationary equilibria of a single-controller stochastic game

Publisher: Springer Science and Business Media LLC

Date: 10-1984

DOI: 10.1007/BF02591936

Deterministic snakes and Ladders Heuristic for the Hamiltonian cycle problem

Publisher: Springer Science and Business Media LLC

Date: 28-09-2014

DOI: 10.1007/S12532-013-0059-2

Linearly-growing reductions of karp's 21 NP-complete problems

Publisher: American Institute of Mathematical Sciences (AIMS)

Date: 2018

DOI: 10.3934/NACO.2018001

A conjecture on the prevalence of cubic bridge graphs

Publisher: University of Zielona Góra, Poland

Date: 2010

DOI: 10.7151/DMGT.1485

Nonlinear programming and stationary strategies in stochastic games

Publisher: Springer Science and Business Media LLC

Date: 03-1986

DOI: 10.1007/BF01580590

Ordered field property for stochastic games when the player who controls transitions changes from state to state

Publisher: Springer Science and Business Media LLC

Date: 08-1981

DOI: 10.1007/BF00935890

A regional allocation of world CO2 emission reductions

Publisher: Elsevier BV

Date: 03-1997

DOI: 10.1016/S0378-4754(97)00009-8

Nonlinear programming and stationary equilibria in stochastic games

Publisher: Springer Science and Business Media LLC

Date: 03-1991

DOI: 10.1007/BF01594936

Control of singularly perturbed hybrid stochastic systems

Publisher: Institute of Electrical and Electronics Engineers (IEEE)

Date: 2001

DOI: 10.1109/9.905686

On the determinant and its derivatives of the rank-one corrected generator of a Markov chain on a graph

Publisher: Springer Science and Business Media LLC

Date: 04-02-2013

DOI: 10.1007/S10898-012-9855-X

Stability analysis and controller design for a class of uncertain systems with Markovian jumping parameters

Publisher: Oxford University Press (OUP)

Date: 06-2000

DOI: 10.1093/IMAMCI/17.2.179

On the puiseux series expansion of the limit discount equation of stochastic games

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Date: 05-1997

DOI: 10.1137/S0363012995284138

Hamiltonian Cycles and Subsets of Discounted Occupational Measures

Publisher: Institute for Operations Research and the Management Sciences (INFORMS)

Date: 05-2020

DOI: 10.1287/MOOR.2019.1009

Abstract: We study a certain polytope arising from embedding the Hamiltonian cycle problem in a discounted Markov decision process. The Hamiltonian cycle problem can be reduced to finding particular extreme points of a certain polytope associated with the input graph. This polytope is a subset of the space of discounted occupational measures. We characterize the feasible bases of the polytope for a general input graph G and determine the expected numbers of different types of feasible bases when the underlying graph is random. We utilize these results to demonstrate that augmenting certain additional constraints to reduce the polyhedral domain can eliminate a large number of feasible bases that do not correspond to Hamiltonian cycles. Finally, we develop a random walk algorithm on the feasible bases of the reduced polytope and present some numerical results. We conclude with a conjecture on the feasible bases of the reduced polytope.

Refined MDP-Based branch-and-fix algorithm for the hamiltonian cycle problem

Publisher: Institute for Operations Research and the Management Sciences (INFORMS)

Date: 08-2009

DOI: 10.1287/MOOR.1090.0398

Abstract: We consider the famous Hamiltonian cycle problem (HCP) embedded in a Markov decision process (MDP). More specifically, we consider the HCP as an optimisation problem over the space of occupation measures induced by the MDP's stationary policies. In recent years, this approach to the HCP has led to a number of alternative formulations and algorithmic approaches. In this paper, we focus on a specific embedding, because of the work of Feinberg. We present a “branch-and-fix” type algorithm that solves the HCP. At each branch of the algorithm, only a linear program needs to be solved and the dimensions of the successive linear programs are shrinking rather than expanding. Because the nodes of the branch-and-fix tree correspond to specially structured 1-randomised policies, we characterise the latter. This characterisation indicates that the total number of such policies is significantly smaller than the subset of all 1-randomised policies. Finally, we present some numerical results.

Games, incompetence, and training

Publisher: Birkhäuser Boston

Date: 2007

DOI: 10.1007/978-0-8176-4553-3_5

A note on using the resistance-distance matrix to solve Hamiltonian cycle problem

Publisher: Springer Science and Business Media LLC

Date: 28-06-2017

DOI: 10.1007/S10479-017-2571-7

Genetic theory for cubic graphs

Publisher: Springer International Publishing

Date: 2015

DOI: 10.1007/978-3-319-19680-0

On the hamiltonicity gap and doubly stochastic matrices

Publisher: Wiley

Date: 10-09-2009

DOI: 10.1002/RSA.20237

Hospital Event Simulation Model: Arrivals to Discharge–Design, development and application

Publisher: Elsevier BV

Date: 11-2016

DOI: 10.1016/J.SIMPAT.2016.07.004

Hamiltonian cycle curves in the space of discounted occupational measures

Publisher: Springer Science and Business Media LLC

Date: 14-10-2015

DOI: 10.1007/S10479-015-2030-2

Percentile Performance Criteria For Limiting Average Markov Decision Processes

Publisher: Institute of Electrical and Electronics Engineers (IEEE)

Date: 1995

DOI: 10.1109/9.362904

Singularly perturbed linear programs and Markov decision processes

Publisher: Elsevier BV

Date: 05-2016

DOI: 10.1016/J.ORL.2016.02.005

Directed graphs, hamiltonicity and doubly stochastic matrices

Publisher: Wiley

Date: 2004

DOI: 10.1002/RSA.20034

Gröbner bases in asymptotic analysis of perturbed polynomial programs

Publisher: Springer Science and Business Media LLC

Date: 20-06-2006

DOI: 10.1007/S00186-006-0073-5

A finite algorithm for the switching control stochastic game

Publisher: Springer Science and Business Media LLC

Date: 03-1983

DOI: 10.1007/BF01720283

Player Aggregation in the Traveling Inspector Model

Publisher: Institute of Electrical and Electronics Engineers (IEEE)

Date: 08-1985

DOI: 10.1109/TAC.1985.1104060

Multivariate polynomial perturbations of algebraic equations

Publisher: Elsevier BV

Date: 09-2010

DOI: 10.1016/J.JMAA.2010.02.026

An asymptotic simplex method for parametric linear programming

Publisher: IEEE

Date: 1999

DOI: 10.1109/IDC.1999.754195

Algorithms for singularly perturbed limiting average markov control problems

Publisher: Institute of Electrical and Electronics Engineers (IEEE)

Date: 1992

DOI: 10.1109/9.159585

How Airlines and Airports Recover from Schedule Perturbations: A Survey

Publisher: Springer Science and Business Media LLC

Date: 2001

DOI: 10.1023/A:1016079600083

Perturbation and stability theory for markov control problems

Publisher: Institute of Electrical and Electronics Engineers (IEEE)

Date: 1992

DOI: 10.1109/9.159584

Decomposition and parallel processing techniques for two-time scale controlled Markov chains

Publisher: IEEE

Date: 2000

DOI: 10.1109/CDC.2000.912851

To fish or cut bait?

Publisher: IEEE

Date: 12-2018

DOI: 10.1109/ASCC.2017.8287563

Inspection optimization model

Publisher: Elsevier BV

Date: 1994

DOI: 10.1016/0038-0121(94)90001-9

Singularly perturbed Markov control problem: Limiting average cost

Publisher: Springer Science and Business Media LLC

Date: 12-1991

DOI: 10.1007/BF02055579

Percentiles and markovian decision processes

Publisher: Elsevier BV

Date: 04-1983

DOI: 10.1016/0167-6377(83)90057-3

Incompetence and impact of training in bimatrix games

Publisher: Elsevier BV

Date: 10-2012

DOI: 10.1016/J.AUTOMATICA.2012.06.046

Sustainability screw: Role of relative production and abatement time scales

Publisher: Informa UK Limited

Date: 08-2015

DOI: 10.1057/JORS.2014.39

Clustering of spectra and fractals of regular graphs

Publisher: Elsevier BV

Date: 09-2007

DOI: 10.1016/J.JMAA.2006.09.072

Hamiltonian transition matrices

Publisher: ACM

Date: 2011

DOI: 10.4108/ICST.VALUETOOLS.2011.245841

A two-factor stochastic production model with two time scales

Publisher: Elsevier BV

Date: 10-2001

DOI: 10.1016/S0005-1098(01)00123-6

Weighted reward criteria in Competitive Markov Decision Processes

Publisher: Springer Science and Business Media LLC

Date: 07-1992

DOI: 10.1007/BF01416234

On transition matrices of Markov chains corresponding to Hamiltonian cycles

Publisher: Springer Science and Business Media LLC

Date: 19-06-2016

DOI: 10.1007/S10479-014-1642-2

Where Do Mistakes Lead? A Survey of Games with Incompetent Players

Publisher: Springer Science and Business Media LLC

Date: 10-02-2022

DOI: 10.1007/S13235-022-00425-3

Abstract: Mathematical models often aim to describe a complicated mechanism in a cohesive and simple manner. However, reaching perfect balance between being simple enough or overly simplistic is a challenging task. Frequently, game-theoretic models have an underlying assumption that players, whenever they choose to execute a specific action, do so perfectly. In fact, it is rare that action execution perfectly coincides with intentions of in iduals, giving rise to behavioural mistakes. The concept of incompetence of players was suggested to address this issue in game-theoretic settings. Under the assumption of incompetence, players have non-zero probabilities of executing a different strategy from the one they chose, leading to stochastic outcomes of the interactions. In this article, we survey results related to the concept of incompetence in classic as well as evolutionary game theory and provide several new results. We also suggest future extensions of the model and argue why it is important to take into account behavioural mistakes when analysing interactions among players in both economic and biological settings.

Algorithms for stochastic games - A survey

Publisher: Springer Science and Business Media LLC

Date: 11-1991

DOI: 10.1007/BF01415989

The image greenhouse model as a mathematical system

Publisher: Elsevier BV

Date: 05-1994

DOI: 10.1016/0307-904X(94)90332-8

Zero-Sum Stochastic Games over the Field of Real Algebraic Numbers

Publisher: Springer Science and Business Media LLC

Date: 25-01-2019

DOI: 10.1007/S13235-018-00293-W

OR/MS and environmental decision making under uncertainty

Publisher: Springer US

Date: 2010

DOI: 10.1007/978-1-4419-1129-2_1

A new heuristic for detecting non-Hamiltonicity in cubic graphs

Publisher: Elsevier BV

Date: 12-2015

DOI: 10.1016/J.COR.2015.06.004

Algorithms for singularly perturbed markov control problems: A survey

Publisher: Elsevier

Date: 1995

DOI: 10.1016/S0090-5267(05)80010-6

An Interior point heuristic for the hamiltonian cycle problem via markov decision processes

Publisher: Springer Science and Business Media LLC

Date: 07-2004

DOI: 10.1023/B:JOGO.0000044772.11089.1A

Weighted Markov decision processes with perturbation

Publisher: Springer Science and Business Media LLC

Date: 07-2001

DOI: 10.1007/S001860100125

Hamiltonian cycles, random walks, and discounted occupational measures

Publisher: Institute for Operations Research and the Management Sciences (INFORMS)

Date: 05-2011

DOI: 10.1287/MOOR.1110.0492

Abstract: We develop a new, random walk-based, algorithm for the Hamiltonian cycle problem. The random walk is on pairs of extreme points of two suitably constructed polytopes. The latter are derived from geometric properties of the space of discounted occupational measures corresponding to a given graph. The algorithm searches for a measure that corresponds to a common extreme point in these two specially constructed polyhedral subsets of that space. We prove that if a given undirected graph is Hamiltonian, then with probability one this random walk algorithm detects its Hamiltonicity in a finite number of iterations. We support these theoretical results by numerical experiments that demonstrate a surprisingly slow growth in the required number of iterations with the size of the given graph.

Mistakes can stabilise the dynamics of rock-paper-scissors games

Publisher: Public Library of Science (PLoS)

Date: 12-04-2021

DOI: 10.1371/JOURNAL.PCBI.1008523

Abstract: A game of rock-paper-scissors is an interesting ex le of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow in iduals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving. We consider two cases: completely random mistakes when in iduals have no bias towards any strategy and a general form of mistakes. Then, we determine conditions for a strategy to dominate all other strategies. However, given that in iduals who adopt a dominating strategy are still prone to behavioural mistakes in the observed behaviour, we may still observe extinct strategies. That is, behavioural mistakes in strategy execution stabilise evolutionary dynamics leading to an evolutionary stable and, potentially, mixed co-existence equilibrium.

Asymptotic analysis of perturbed mathematical programs

Publisher: Elsevier BV

Date: 11-2000

DOI: 10.1006/JMAA.2000.7025

Communicating MDPs: Equivalence and LP properties

Publisher: Elsevier BV

Date: 12-1988

DOI: 10.1016/0167-6377(88)90062-4

A Projection-Adapted Cross Entropy (PACE) method for transmission network planning

Publisher: Springer Science and Business Media LLC

Date: 05-2011

DOI: 10.1007/S12667-011-0033-X

Semi-infinite Markov decision processes

Publisher: Springer Science and Business Media LLC

Date: 17-02-2000

DOI: 10.1007/S001860050006

Evolutionary games under incompetence

Publisher: Springer Science and Business Media LLC

Date: 26-02-2018

DOI: 10.1007/S00285-018-1221-2

Abstract: The adaptation process of a species to a new environment is a significant area of study in biology. As part of natural selection, adaptation is a mutation process which improves survival skills and reproductive functions of species. Here, we investigate this process by combining the idea of incompetence with evolutionary game theory. In the sense of evolution, incompetence and training can be interpreted as a special learning process. With focus on the social side of the problem, we analyze the influence of incompetence on behavior of species. We introduce an incompetence parameter into a learning function in a single-population game and analyze its effect on the outcome of the replicator dynamics. Incompetence can change the outcome of the game and its dynamics, indicating its significance within what are inherently imperfect natural systems.

Stochasticity in the image greenhouse model

Publisher: Elsevier BV

Date: 11-1995

DOI: 10.1016/0895-7177(95)00176-3

A hybrid simulation-optimization algorithm for the Hamiltonian cycle problem

Publisher: Springer Science and Business Media LLC

Date: 21-05-2011

DOI: 10.1007/S10479-009-0565-9

University Of Queensland

Location: Australia

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Monash University

Location: Australia

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University Of Melbourne

Location: Australia

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University Of Illinois At Chicago

Location: United States of America

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Linkage Projects - Grant ID: LP130100323

Start Date: 04-2014

End Date: 06-2017

Amount: $215,733.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP0666632

Start Date: 2006

End Date: 06-2011

Amount: $560,000.00

Funder: Australian Research Council

Linkage - International - Grant ID: LX0881972

Start Date: 07-2009

End Date: 12-2012

Amount: $46,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP120100532

Start Date: 2012

End Date: 12-2015

Amount: $395,000.00

Funder: Australian Research Council

Linkage - International - Grant ID: LX0560049

Start Date: 2005

End Date: 11-2011

Amount: $62,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP180101602

Start Date: 04-2018

End Date: 09-2023

Amount: $386,828.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP0987148

Start Date: 2009

End Date: 12-2011

Amount: $240,000.00

Funder: Australian Research Council

Linkage Projects - Grant ID: LP0884005

Start Date: 07-2008

End Date: 03-2012

Amount: $160,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP0343028

Start Date: 2003

End Date: 12-2005

Amount: $172,536.00

Funder: Australian Research Council

Special Research Initiatives - Grant ID: SR0354553

Start Date: 01-2004

End Date: 12-2003

Amount: $30,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP160101236

Start Date: 04-2016

End Date: 08-2019

Amount: $388,294.00

Funder: Australian Research Council

Special Research Initiatives - Grant ID: SR0354727

Start Date: 2003

End Date: 12-2003

Amount: $20,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP200101049

Start Date: 05-2021

End Date: 12-2024

Amount: $365,000.00

Funder: Australian Research Council

Special Research Initiatives - Grant ID: SR0354558

Start Date: 2003

End Date: 12-2003

Amount: $10,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP220102101

Start Date: 2022

End Date: 03-2023

Amount: $383,000.00

Funder: Australian Research Council