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Journal articles on the topic 'Two-person zero-sum games'

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Published: 4 June 2021
Last updated: 13 February 2022

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1

Baykal-Gürsoy, Melike. "Two-person zero-sum stochastic games." Annals of Operations Research 28, no. 1 (December 1991): 135–52. http://dx.doi.org/10.1007/bf02055578.

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2

Lal, Arbind K., and Sagnik Sinha. "Zero-sum two-person semi-Markov games." Journal of Applied Probability 29, no. 1 (March 1992): 56–72. http://dx.doi.org/10.2307/3214791.

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Semi-Markov games are investigated under discounted and limiting average payoff criteria. The issue of the existence of the value and a pair of stationary optimal strategies are settled; the optimality equation is studied and under a natural ergodic condition the existence of a solution to the optimality equation is proved for the limiting average case. Semi-Markov games provide useful flexibility in constructing recursive game models. All the work on Markov/semi-Markov decision processes and Markov (stochastic) games can be viewed as special cases of the developments in this paper.
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3

Lal, Arbind K., and Sagnik Sinha. "Zero-sum two-person semi-Markov games." Journal of Applied Probability 29, no. 01 (March 1992): 56–72. http://dx.doi.org/10.1017/s002190020010662x.

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Semi-Markov games are investigated under discounted and limiting average payoff criteria. The issue of the existence of the value and a pair of stationary optimal strategies are settled; the optimality equation is studied and under a natural ergodic condition the existence of a solution to the optimality equation is proved for the limiting average case. Semi-Markov games provide useful flexibility in constructing recursive game models. All the work on Markov/semi-Markov decision processes and Markov (stochastic) games can be viewed as special cases of the developments in this paper.
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4

Yang, Yan Mei, Yan Guo, Li Chao Feng, and Jian Yong Di. "Solving Two-Person Zero-Sum Game by Matlab." Applied Mechanics and Materials 50-51 (February 2011): 262–65. http://dx.doi.org/10.4028/www.scientific.net/amm.50-51.262.

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In this article we present an overview on two-person zero-sum games, which play a central role in the development of the theory of games. Two-person zero-sum games is a special class of game theory in which one player wins what the other player loses with only two players. It is difficult to solve 2-person matrix game with the order m×n(m≥3,n≥3). The aim of the article is to determine the method on how to solve a 2-person matrix game by linear programming function linprog() in matlab. With linear programming techniques in the Matlab software, we present effective method for solving large zero-sum games problems.
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5

Llewellyn, Donna Crystal, Craig Tovey, and Michael Trick. "Finding Saddlepoints of Two-Person, Zero Sum Games." American Mathematical Monthly 95, no. 10 (December 1988): 912. http://dx.doi.org/10.2307/2322384.

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6

Llewellyn, Donna Crystal, Craig Tovey, and Michael Trick. "Finding Saddlepoints of Two-Person, Zero Sum Games." American Mathematical Monthly 95, no. 10 (December 1988): 912–18. http://dx.doi.org/10.1080/00029890.1988.11972116.

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7

Washburn, Alan, and Kevin Wood. "Two-Person Zero-Sum Games for Network Interdiction." Operations Research 43, no. 2 (April 1995): 243–51. http://dx.doi.org/10.1287/opre.43.2.243.

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8

Forges, Francoise. "Correlated Equilibrium in Two-Person Zero-Sum Games." Econometrica 58, no. 2 (March 1990): 515. http://dx.doi.org/10.2307/2938215.

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9

Laraki, R., A. P. Maitra, and W. D. Sudderth. "Two-Person Zero-Sum Stochastic Games with Semicontinuous Payoff." Dynamic Games and Applications 3, no. 2 (September 5, 2012): 162–71. http://dx.doi.org/10.1007/s13235-012-0054-7.

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10

Hyeong Soo Chang and S. I. Marcus. "Two-person zero-sum markov games: receding horizon approach." IEEE Transactions on Automatic Control 48, no. 11 (November 2003): 1951–61. http://dx.doi.org/10.1109/tac.2003.819077.

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11

Sun, Jingrui. "Two-Person Zero-Sum Stochastic Linear-Quadratic Differential Games." SIAM Journal on Control and Optimization 59, no. 3 (January 2021): 1804–29. http://dx.doi.org/10.1137/20m1340368.

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12

Wu, Xiao, Qi Wang, and Yinying Kong. "Two-person zero-sum stochastic games with varying discount factors." AIMS Mathematics 6, no. 10 (2021): 11516–29. http://dx.doi.org/10.3934/math.2021668.

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<abstract><p>In this paper, two-person zero-sum Markov games with Borel state space and action space, unbounded reward function and state-dependent discount factors are studied. The optimal criterion is expected discount criterion. Firstly, sufficient conditions for the existence of optimal policies are given for the two-person zero-sum Markov games with varying discount factors. Then, the existence of optimal policies is proved by Banach fixed point theorem. Finally, we give an example for reservoir operations to illustrate the existence results.</p></abstract>
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13

Avşar, Zeynep Müge, and Melike Baykal-Gürsoy. "A note on two-person zero-sum communicating stochastic games." Operations Research Letters 34, no. 4 (July 2006): 412–20. http://dx.doi.org/10.1016/j.orl.2005.07.008.

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14

Lin, Xiaomin, Peter A. Beling, and Randy Cogill. "Multiagent Inverse Reinforcement Learning for Two-Person Zero-Sum Games." IEEE Transactions on Games 10, no. 1 (March 2018): 56–68. http://dx.doi.org/10.1109/tciaig.2017.2679115.

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15

Nawaz, Ahmad, and A. H. Toor. "Generalized quantization scheme for two-person non-zero sum games." Journal of Physics A: Mathematical and General 37, no. 47 (November 11, 2004): 11457–63. http://dx.doi.org/10.1088/0305-4470/37/47/014.

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16

Radzik, Tadeusz. "Nash equilibria of discontinuous non-zero-sum two-person games." International Journal of Game Theory 21, no. 4 (December 1993): 429–37. http://dx.doi.org/10.1007/bf01240157.

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17

Chang, Hyeong Soo. "Value set iteration for two-person zero-sum Markov games." Automatica 76 (February 2017): 61–64. http://dx.doi.org/10.1016/j.automatica.2016.10.010.

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18

Kreines, E. M., N. M. Novikova, and I. I. Pospelova. "Equilibria and Compromises in Two-Person Zero-Sum Multicriteria Games." Journal of Computer and Systems Sciences International 59, no. 6 (November 2020): 871–93. http://dx.doi.org/10.1134/s1064230720060088.

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19

K, Selvakumari. "Characterization of Nash Equilibrium Strategy of a Two Person Non Zero Sum Games with Trapezoidal Fuzzy Payoffs." International Journal of Psychosocial Rehabilitation 24, no. 4 (February 28, 2020): 4895–902. http://dx.doi.org/10.37200/ijpr/v24i4/pr201590.

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20

Mondal, Prasenjit. "Linear Programming and Zero-Sum Two-Person Undiscounted Semi-Markov Games." Asia-Pacific Journal of Operational Research 32, no. 06 (December 2015): 1550043. http://dx.doi.org/10.1142/s0217595915500438.

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In this paper, zero-sum two-person finite undiscounted (limiting average) semi-Markov games (SMGs) are considered. We prove that the solutions of the game when both players are restricted to semi-Markov strategies are solutions for the original game. In addition, we show that if one player fixes a stationary strategy, then the other player can restrict himself in solving an undiscounted semi-Markov decision process associated with that stationary strategy. The undiscounted SMGs are also studied when the transition probabilities and the transition times are controlled by a fixed player in all states. If such games are unichain, we prove that the value and optimal stationary strategies of the players can be obtained from an optimal solution of a linear programming algorithm. We propose a realistic and generalized traveling inspection model that suitably fits into the class of one player control undiscounted unichain semi-Markov games.
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21

Zhou, Shao Wei. "Two-Person Zero-Sum Stochastic Differential Games for Discrete-Time Systems." Advanced Materials Research 433-440 (January 2012): 3510–13. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.3510.

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This paper discusses two-person zero-sum stochastic differential games for discrete-time systems. The controls for both players are allowed to appear in both the drift and diffusion of the state equation, the weighting matrices in payoff/cost functional are not assumed to be definite. A generalized difference Riccati equation is introduced and the relationship between solvability of the equation and the existence of the saddle point has been given. Furthermore, making use of upper and lower solutions to Riccati equation, we obtained some other results.
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22

Zhang, Pingjian. "Some Results On Two-Person Zero-Sum Linear Quadratic Differential Games." SIAM Journal on Control and Optimization 43, no. 6 (January 2005): 2157–65. http://dx.doi.org/10.1137/s036301290342560x.

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23

Yano, Hitoshi, and Ichiro Nishizaki. "Interactive Fuzzy Approaches for Solving Multiobjective Two-Person Zero-Sum Games." Applied Mathematics 07, no. 05 (2016): 387–98. http://dx.doi.org/10.4236/am.2016.75036.

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24

Koller, Daphne, and Nimrod Megiddo. "The complexity of two-person zero-sum games in extensive form." Games and Economic Behavior 4, no. 4 (October 1992): 528–52. http://dx.doi.org/10.1016/0899-8256(92)90035-q.

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25

Polowczuk, Wojciech. "Pure Nash equilibria in finite two-person non-zero-sum games." International Journal of Game Theory 32, no. 2 (December 1, 2003): 229–40. http://dx.doi.org/10.1007/s001820300155.

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26

Avsar, Zeynep Müge, and Melike Baykal-Gürsoy. "A decomposition approach for undiscounted two-person zero-sum stochastic games." Mathematical Methods of Operations Research (ZOR) 49, no. 3 (July 2, 1999): 483–500. http://dx.doi.org/10.1007/s001860050063.

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27

MEERTENS, MARC, JOS POTTERS, and HANS REIJNIERSE. "DYNAMIC SELECTION IN NORMAL-FORM GAMES." International Game Theory Review 08, no. 03 (September 2006): 395–416. http://dx.doi.org/10.1142/s0219198906000989.

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This paper investigates a class of dynamic selection processes for n-person normal-form games which includes the Brown-von Neumann-Nash dynamics. For (two-person) zero-sum games and for (n-person) potential games every limit set of these dynamics is a subset of the set of Nash-equilibria. Furthermore, under these dynamics the unique Nash-component of a zero-sum game is minimal asymptotically stable and for a potential game a smoothly connected component which is a local maximizer is minimal asymptotically stable.
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28

Tanaka, Tamaki, and Masakazu Higuchi. "Classification of Matrix Types for Multicriteria Two-Person Zero-Sum Matrix Games." IFAC Proceedings Volumes 33, no. 16 (July 2000): 659–68. http://dx.doi.org/10.1016/s1474-6670(17)39712-4.

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29

VAN DER GENUGTEN, BEN. "A WEAKENED FORM OF FICTITIOUS PLAY IN TWO-PERSON ZERO-SUM GAMES." International Game Theory Review 02, no. 04 (December 2000): 307–28. http://dx.doi.org/10.1142/s0219198900000202.

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Fictitious play can be seen as a numerical iteration procedure for determining the value of a game and corresponding optimal strategies. Although convergence is slow, it needs only a modest computer storage. Therefore it seems to be a good way for analysing large games. In this paper we introduce a weakened form of fictitious play, where players at each stage do not have to make the best choice against the total of past choices of the other player but only an increasingly better one. Theoretical bounds for convergence are derived. Furthermore, it is shown that this new form can speed up convergence considerably in practice. It is seen that weakened fictitious play can be extended to models in which the game matrix itself becomes better known as the number of stages increases.
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30

Xu, Jiuping, and Liming Yao. "A Class of Two-Person Zero-Sum Matrix Games with Rough Payoffs." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–22. http://dx.doi.org/10.1155/2010/404792.

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We concentrate on discussing a class of two-person zero-sum games with rough payoffs. Based on the expected value operator and the trust measure of rough variables, the expected equilibrium strategy andr-trust maximin equilibrium strategy are defined. Five cases whether the game existsr-trust maximin equilibrium strategy are discussed, and the technique of genetic algorithm is applied to find the equilibrium strategies. Finally, a numerical example is provided to illustrate the practicality and effectiveness of the proposed technique.
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31

Radzik, Tadeusz. "Pure-strategy ε-Nash equilibrium in two-person non-zero-sum games." Games and Economic Behavior 3, no. 3 (August 1991): 356–67. http://dx.doi.org/10.1016/0899-8256(91)90034-c.

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32

Byrne, C. C., and L. N. Vaserstein. "An improved algorithm for finding saddlepoints of two-person zero-sum games." International Journal of Game Theory 20, no. 2 (June 1991): 149–59. http://dx.doi.org/10.1007/bf01240275.

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33

Carmona, Guilherme, and Luís Carvalho. "Repeated two-person zero-sum games with unequal discounting and private monitoring." Journal of Mathematical Economics 63 (March 2016): 131–38. http://dx.doi.org/10.1016/j.jmateco.2016.02.005.

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34

Ammar, El-Saeed, M. G. Brikaa, and Entsar Abdel-Rehim. "A study on two-person zero-sum rough interval continuous differential games." OPSEARCH 56, no. 3 (June 4, 2019): 689–716. http://dx.doi.org/10.1007/s12597-019-00383-2.

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35

Chang, Hyeong Soo. "Perfect information two-person zero-sum markov games with imprecise transition probabilities." Mathematical Methods of Operations Research 64, no. 2 (July 21, 2006): 335–51. http://dx.doi.org/10.1007/s00186-006-0081-5.

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36

Salamon, David, and Peter Salamon. "Cycling Co-Evolution Resulting from Genetic Adaptation in Two-Person Zero-Sum Games." Open Systems & Information Dynamics 12, no. 03 (September 2005): 265–71. http://dx.doi.org/10.1007/s11080-005-0924-1.

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We consider two populations co-evolving with fitness defined by the payoff in a two-person zero-sum game. We show that such situations lead to spontaneous and sustained oscillations iff the optimal strategy of the game is mixed.
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37

Boros, Endre, Khaled Elbassioni, Vladimir Gurvich, and Kazuhisa Makino. "A Potential Reduction Algorithm for Two-Person Zero-Sum Mean Payoff Stochastic Games." Dynamic Games and Applications 8, no. 1 (July 8, 2016): 22–41. http://dx.doi.org/10.1007/s13235-016-0199-x.

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38

Mondal, Prasenjit. "On zero-sum two-person undiscounted semi-Markov games with a multichain structure." Advances in Applied Probability 49, no. 3 (September 2017): 826–49. http://dx.doi.org/10.1017/apr.2017.23.

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Abstract Zero-sum two-person finite undiscounted (limiting ratio average) semi-Markov games (SMGs) are considered with a general multichain structure. We derive the strategy evaluation equations for stationary strategies of the players. A relation between the payoff in the multichain SMG and that in the associated stochastic game (SG) obtained by a data-transformation is established. We prove that the multichain optimality equations (OEs) for an SMG have a solution if and only if the associated SG has optimal stationary strategies. Though the solution of the OEs may not be optimal for an SMG, we establish the significance of studying the OEs for a multichain SMG. We provide a nice example of SMGs in which one player has no optimal strategy in the stationary class but has an optimal semistationary strategy (that depends only on the initial and current state of the game). For an SMG with absorbing states, we prove that solutions in the game where all players are restricted to semistationary strategies are solutions for the unrestricted game. Finally, we prove the existence of stationary optimal strategies for unichain SMGs and conclude that the unichain condition is equivalent to require that the game satisfies some recurrence/ergodicity/weakly communicating conditions.
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39

Hyeong Soo Chang, Jiaqiao Hu, M. C. Fu, and S. I. Marcus. "Adaptive Adversarial Multi-Armed Bandit Approach to Two-Person Zero-Sum Markov Games." IEEE Transactions on Automatic Control 55, no. 2 (February 2010): 463–68. http://dx.doi.org/10.1109/tac.2009.2036333.

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40

Qiu, Hong, and Jiongmin Yong. "Hamilton–Jacobi equations and two-person zero-sum differential games with unbounded controls." ESAIM: Control, Optimisation and Calculus of Variations 19, no. 2 (January 23, 2013): 404–37. http://dx.doi.org/10.1051/cocv/2012015.

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41

Sun, Jingrui, Jiongmin Yong, and Shuguang Zhang. "Linear quadratic stochastic two-person zero-sum differential games in an infinite horizon." ESAIM: Control, Optimisation and Calculus of Variations 22, no. 3 (May 16, 2016): 743–69. http://dx.doi.org/10.1051/cocv/2015024.

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42

YANO, Hitoshi, and Ichiro NISHIZAKI. "A fuzzy approach for multiobjective two-person zero-sum games with fuzzy payoff matrices." Journal of Japan Society for Fuzzy Theory and Intelligent Informatics 28, no. 4 (2016): 756–63. http://dx.doi.org/10.3156/jsoft.28.756.

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43

Dutta, Bapi, and S. K. Gupta. "On Nash Equilibrium Strategy of Two-person Zero-sum Games with Trapezoidal Fuzzy Payoffs." Fuzzy Information and Engineering 6, no. 3 (September 2014): 299–314. http://dx.doi.org/10.1016/j.fiae.2014.12.003.

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44

Ramachandran, K. M., and A. N. V. Rao. "Differential inequality approach for deterministic approximation in two person zero-sum stochastic differential games." Nonlinear Analysis: Theory, Methods & Applications 63, no. 5-7 (November 2005): e1999-e2008. http://dx.doi.org/10.1016/j.na.2005.03.009.

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45

Chang, Hyeong Soo. "A Necessary Condition for Nash Equilibrium in Two-Person Zero-Sum Constrained Stochastic Games." Game Theory 2013 (December 9, 2013): 1–5. http://dx.doi.org/10.1155/2013/290427.

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46

Ziad, Abderrahmane. "Pure strategy Nash equilibria of non-zero-sum two-person games: non-convex case." Economics Letters 62, no. 3 (March 1999): 307–10. http://dx.doi.org/10.1016/s0165-1765(98)00246-8.

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47

Lorenzo, José María, Ismael Hernández-Noriega, and Tomás Prieto-Rumeau. "Approximation of two-person zero-sum continuous-time Markov games with average payoff criterion." Operations Research Letters 43, no. 1 (January 2015): 110–16. http://dx.doi.org/10.1016/j.orl.2014.12.004.

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48

Maeda, Takashi. "On characterization of equilibrium strategy of two-person zero-sum games with fuzzy payoffs." Fuzzy Sets and Systems 139, no. 2 (October 2003): 283–96. http://dx.doi.org/10.1016/s0165-0114(02)00509-2.

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49

Mou, Libin, and Jiongmin Yong. "Two-person zero-sum linear quadratic stochastic differential games by a Hilbert space method." Journal of Industrial & Management Optimization 2, no. 1 (2006): 95–117. http://dx.doi.org/10.3934/jimo.2006.2.95.

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50

Chang, Hyeong Soo. "Converging Coevolutionary Algorithm for Two-Person Zero-Sum Discounted Markov Games With Perfect Information." IEEE Transactions on Automatic Control 53, no. 2 (March 2008): 596–601. http://dx.doi.org/10.1109/tac.2007.914299.

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