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Journal articles on the topic 'Differential games'

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Published: 4 June 2021
Last updated: 30 July 2024

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1

Platzer, André. "Differential Hybrid Games." ACM Transactions on Computational Logic 18, no. 3 (August 21, 2017): 1–44. http://dx.doi.org/10.1145/3091123.

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2

Quincampoix, Marc. "Playable differential games." Journal of Mathematical Analysis and Applications 161, no. 1 (October 1991): 194–211. http://dx.doi.org/10.1016/0022-247x(91)90369-b.

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3

Smolyakov, É. R. "Multicriterion differential games." Cybernetics and Systems Analysis 30, no. 1 (January 1994): 10–17. http://dx.doi.org/10.1007/bf02366357.

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4

Bressan, Alberto. "Noncooperative Differential Games." Milan Journal of Mathematics 79, no. 2 (August 28, 2011): 357–427. http://dx.doi.org/10.1007/s00032-011-0163-6.

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5

Pei, Hai-Long, and Ming-An Tong. "Team Differential Games." IFAC Proceedings Volumes 23, no. 8 (August 1990): 433–37. http://dx.doi.org/10.1016/s1474-6670(17)51954-0.

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6

Serea, Oana-Silvia. "Reflected Differential Games." SIAM Journal on Control and Optimization 48, no. 4 (January 2009): 2516–32. http://dx.doi.org/10.1137/080739215.

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7

Fonseca-Morales, Alejandra, and Onésimo Hernández-Lerma. "Potential Differential Games." Dynamic Games and Applications 8, no. 2 (April 3, 2017): 254–79. http://dx.doi.org/10.1007/s13235-017-0218-6.

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8

Yong, Jiongmin. "On Differential Evasion Games." SIAM Journal on Control and Optimization 26, no. 1 (January 1988): 1–22. http://dx.doi.org/10.1137/0326001.

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9

Yong, Jiongmin. "On Differential Pursuit Games." SIAM Journal on Control and Optimization 26, no. 2 (March 1988): 478–95. http://dx.doi.org/10.1137/0326029.

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10

Browne, Sid. "Stochastic differential portfolio games." Journal of Applied Probability 37, no. 1 (March 2000): 126–47. http://dx.doi.org/10.1239/jap/1014842273.

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We study stochastic dynamic investment games in continuous time between two investors (players) who have available two different, but possibly correlated, investment opportunities. There is a single payoff function which depends on both investors’ wealth processes. One player chooses a dynamic portfolio strategy in order to maximize this expected payoff, while his opponent is simultaneously choosing a dynamic portfolio strategy so as to minimize the same quantity. This leads to a stochastic differential game with controlled drift and variance. For the most part, we consider games with payoffs that depend on the achievement of relative performance goals and/or shortfalls. We provide conditions under which a game with a general payoff function has an achievable value, and give an explicit representation for the value and resulting equilibrium portfolio strategies in that case. It is shown that non-perfect correlation is required to rule out trivial solutions. We then use this general result explicitly to solve a variety of specific games. For example, we solve a probability maximizing game, where each investor is trying to maximize the probability of beating the other's return by a given predetermined percentage. We also consider objectives related to the minimization or maximization of the expected time until one investor's return beats the other investor's return by a given percentage. Our results allow a new interpretation of the market price of risk in a Black-Scholes world. Games with discounting are also discussed, as are games of fixed duration related to utility maximization.
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11

Browne, Sid. "Stochastic differential portfolio games." Journal of Applied Probability 37, no. 01 (March 2000): 126–47. http://dx.doi.org/10.1017/s0021900200015308.

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We study stochastic dynamic investment games in continuous time between two investors (players) who have available two different, but possibly correlated, investment opportunities. There is a single payoff function which depends on both investors’ wealth processes. One player chooses a dynamic portfolio strategy in order to maximize this expected payoff, while his opponent is simultaneously choosing a dynamic portfolio strategy so as to minimize the same quantity. This leads to a stochastic differential game with controlled drift and variance. For the most part, we consider games with payoffs that depend on the achievement of relative performance goals and/or shortfalls. We provide conditions under which a game with a general payoff function has an achievable value, and give an explicit representation for the value and resulting equilibrium portfolio strategies in that case. It is shown that non-perfect correlation is required to rule out trivial solutions. We then use this general result explicitly to solve a variety of specific games. For example, we solve a probability maximizing game, where each investor is trying to maximize the probability of beating the other's return by a given predetermined percentage. We also consider objectives related to the minimization or maximization of the expected time until one investor's return beats the other investor's return by a given percentage. Our results allow a new interpretation of the market price of risk in a Black-Scholes world. Games with discounting are also discussed, as are games of fixed duration related to utility maximization.
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12

Wrzaczek, Stefan, Edward H. Kaplan, Jonathan P. Caulkins, Andrea Seidl, and Gustav Feichtinger. "Differential Terror Queue Games." Dynamic Games and Applications 7, no. 4 (May 28, 2016): 578–93. http://dx.doi.org/10.1007/s13235-016-0195-1.

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13

Mehlmann, Alexander. "Diffeomorphisms and differential games." European Journal of Operational Research 24, no. 1 (January 1986): 85–90. http://dx.doi.org/10.1016/0377-2217(86)90013-5.

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14

Berkovitz, Leonard D. "Differential games of survival." Journal of Mathematical Analysis and Applications 129, no. 2 (February 1988): 493–504. http://dx.doi.org/10.1016/0022-247x(88)90267-3.

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15

Fleming, W. H., and M. Nisio. "Differential games for stochastic partial differential equations." Nagoya Mathematical Journal 131 (September 1993): 75–107. http://dx.doi.org/10.1017/s0027763000004554.

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In this paper we are concerned with zero-sum two-player finite horizon games for stochastic partial differential equations (SPDE in short). The main aim is to formulate the principle of dynamic programming for the upper (or lower) value function and investigate the relationship between upper (or lower) value function and viscocity solution of min-max (or max-min) equation on Hilbert space.
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16

Wang, Jiali, Xin Jin, and Yang Tang. "Optimal strategy analysis for adversarial differential games." Electronic Research Archive 30, no. 10 (2022): 3692–710. http://dx.doi.org/10.3934/era.2022189.

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<abstract><p>Optimal decision-making and winning-regions analysis in adversarial differential games are challenging theoretical problems because of the complex interactions between players. To solve these problems, we present an organized review for pursuit-evasion games, reach-avoid games and capture-the-flag games; we also outline recent developments in three types of games. First, we summarize recent results for pursuit-evasion games and classify them according to different numbers of players. As a special kind of pursuit-evasion games, target-attacker-defender games with an active target are analyzed from the perspectives of different speed ratios for players. Second, the related works for reach-avoid games and capture-the-flag games are compared in terms of analytical methods and geometric methods, respectively. These methods have different effects on the barriers and optimal strategy analysis between players. Future directions for the pursuit-evasion games, reach-avoid games, capture-the-flag games and their applications are discussed in the end.</p></abstract>
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17

Trafalis, Theodore B., and Thomas L. Morin. "A differential dynamic programming algorithm for differential games." Optimal Control Applications and Methods 22, no. 1 (January 2001): 17–36. http://dx.doi.org/10.1002/oca.680.

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18

Bardan, Andrii, and Yaroslav Bihun. "Computer modeling of differential games." Modeling Control and Information Technologies, no. 5 (November 21, 2021): 16–18. http://dx.doi.org/10.31713/mcit.2021.03.

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This paper uses differential games for viewing with simple movement and gives examples of viewing processes. The software has been developed and computer modeling of several methods of interaction in a conflict-driven environment has been introduced.
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19

Smol’yakov, E. R. "Combined equilibrium for differential games." Differential Equations 51, no. 11 (November 2015): 1484–92. http://dx.doi.org/10.1134/s0012266115110099.

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20

Aubin, Jean-Pierre. "Differential Games: A Viability Approach." SIAM Journal on Control and Optimization 28, no. 6 (November 1990): 1294–320. http://dx.doi.org/10.1137/0328069.

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21

Ghosh, Mrinal K., and K. S. Mallikarjuna Rao. "Differential Games with Ergodic Payoff." SIAM Journal on Control and Optimization 43, no. 6 (January 2005): 2020–35. http://dx.doi.org/10.1137/s0363012903404511.

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22

Qian, Xiaojun. "Differential Games with Information Lags." SIAM Journal on Control and Optimization 32, no. 3 (May 1994): 808–30. http://dx.doi.org/10.1137/s0363012991202379.

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23

Grüne, Lars, and Oana Silvia Serea. "Differential Games and Zubov's Method." SIAM Journal on Control and Optimization 49, no. 6 (January 2011): 2349–77. http://dx.doi.org/10.1137/100787829.

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24

Yong, Jiongmin. "Differential games with switching strategies." Journal of Mathematical Analysis and Applications 145, no. 2 (January 1990): 455–69. http://dx.doi.org/10.1016/0022-247x(90)90413-a.

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25

Ostapenko, V. V., and O. M. Timoshenko. "Differential games with random noise." Journal of Mathematical Sciences 97, no. 2 (November 1999): 3952–58. http://dx.doi.org/10.1007/bf02366386.

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26

Williams, Stephen A., and Richard C. Scalzo. "Differential games and BV functions." Journal of Differential Equations 59, no. 3 (September 1985): 296–313. http://dx.doi.org/10.1016/0022-0396(85)90143-3.

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27

Ivanov, G. Ye. "Differential games with ellipsoidal penalties." Journal of Applied Mathematics and Mechanics 68, no. 5 (January 2004): 647–64. http://dx.doi.org/10.1016/j.jappmathmech.2004.09.002.

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28

Youness, E., J. B. Hughes, and N. A. El-Kholy. "Parametric nash coalitive differential games." Mathematical and Computer Modelling 26, no. 2 (July 1997): 97–105. http://dx.doi.org/10.1016/s0895-7177(97)00125-8.

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29

Barron, E. N. "Differential games with maximum cost." Nonlinear Analysis: Theory, Methods & Applications 14, no. 11 (June 1990): 971–89. http://dx.doi.org/10.1016/0362-546x(90)90113-u.

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30

Bressan, Alberto, and Fabio S. Priuli. "Infinite horizon noncooperative differential games." Journal of Differential Equations 227, no. 1 (August 2006): 230–57. http://dx.doi.org/10.1016/j.jde.2006.01.005.

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31

Ivanov, R. P. "MEASURABLE STRATEGIES IN DIFFERENTIAL GAMES." Mathematics of the USSR-Sbornik 66, no. 1 (February 28, 1990): 127–43. http://dx.doi.org/10.1070/sm1990v066n01abeh001167.

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32

Cardaliaguet, P. "Differential Games with Asymmetric Information." SIAM Journal on Control and Optimization 46, no. 3 (January 2007): 816–38. http://dx.doi.org/10.1137/060654396.

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33

Barron, E. N. "Differential Games in $$L^{\infty }$$." Dynamic Games and Applications 7, no. 2 (March 1, 2016): 157–84. http://dx.doi.org/10.1007/s13235-016-0183-5.

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34

Tolwinski, B., A. Haurie, and G. Leitmann. "Cooperative equilibria in differential games." Journal of Mathematical Analysis and Applications 119, no. 1-2 (October 1986): 182–202. http://dx.doi.org/10.1016/0022-247x(86)90152-6.

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35

Grigorenko, N. L., Yu N. Kiselev, N. V. Lagunova, D. B. Silin, and N. G. Trin'ko. "Solution methods for differential games." Computational Mathematics and Modeling 7, no. 1 (1996): 101–16. http://dx.doi.org/10.1007/bf01128750.

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36

Bensoussan, Alain, Jens Frehse, and Jens Vogelgesang. "Nash and Stackelberg differential games." Chinese Annals of Mathematics, Series B 33, no. 3 (May 2012): 317–32. http://dx.doi.org/10.1007/s11401-012-0716-1.

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37

Zhukovskiy, V. I., L. V. Zhukovskaya, K. N. Kudryavtsev, and V. E. Romanova. "ON ONE MODIFICATION OF NASH EQUILIBRIUM." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 14, no. 2 (2022): 13–30. http://dx.doi.org/10.14529/mmph220202.

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By the end of the last century there were four areas in the mathematical theory of positional differential games: non-coalitional positional differential games, cooperative, hierarchical and, finally, the least-understood coalitional positional differential games. In their turn, coalitional games are divided into games with transferable payoffs (games with side payments when players can split profits in the course of the game) and with non-transferable payoffs (games with side payments when there are no such distributions for this or that reason). The coalitional games with side payments are being extensively explored at the Faculties of Applied Mathematics and Management Processes of St. Petersburg University and the Institute of Mathematics and Information Technologies of Petrozavodsk State University (by Professors L.A. Petrosyan, V.V. Mozalov, E.M. Parilina, A.N. Rettieva and their numerous students). However, side payments are not always present even in economic cooperation; moreover, side payments can be legislated against. We believe that the research of the equilibrium of threats and counter-threats (sanctions and counter-sanctions) in non-coalitional differential games that we have carried out over the last years allows to also cover some aspects of non-transferable payoff coalitional games. The article considers the issues of namely the internal and external stability of coalitions in the class of positional differential games. The coefficient constraints were identified for the mathematical model of a linear-quadratic differential positional game with twin-coalitional structure for six persons where this coalitional structure is internally and externally stable.
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38

Kassem, Mohamed Abd El-Hady, Nabil A. El-kholy, M. H. Eid, and Mohamed M. M. Ibrahim. "On Nash-Coalitive Fuzzy Continuous Differential Games." International Journal of Emerging Technology and Advanced Engineering 12, no. 3 (March 11, 2022): 24–32. http://dx.doi.org/10.46338/ijetae0322_04.

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This paper concentrates on providing a simple and effective technique to solve the Nash-coalitive fuzzy continuous differential games. These games are featured by having fuzzy coefficients, fuzzy controls, and fuzzy state functions. The proposed technique utilizes the α-cut set concept of fuzzy numbers to transform the problem under study into a corresponding interval problem. The latter one is sliced into two problems, lower problem and upper problem, to obtain the optimal solution for the Nash-coalitive fuzzy continuous differential games problem in a range form. The sufficient and necessary conditions for this problem are derived. A numerical example is provided to clarify the presented concepts. Keywords— fuzzy control, fuzzy differential games, fuzzy numbers, Nash-coalitive differential games
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39

Zhukovskiy, V. I., L. V. Zhukovskaya, S. N. Sachkov, and E. N. Sachkova. "Coalitional Pareto optimal solution of one differential game." Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta 63 (May 2024): 18–36. http://dx.doi.org/10.35634/2226-3594-2024-63-02.

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This paper is devoted to the differential positional coalitional games with non-transferable payoffs (games without side payments). We believe that the researches of the objection and counter-objection equilibrium for non-cooperative differential games that have been carried out over the last years allow to cover some aspects of non-transferable payoff coalitional games. In this paper we consider the issues of the internal and external stability of coalitions in the class of positional differential games. For a differential positional linear-quadratic six-player game with a two-coalitional structure, the coefficient constraints are obtained which provide an internal and external stability of the coalitional structure.
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40

Draouil, Olfa, and Bernt Øksendal. "Stochastic differential games with inside information." Infinite Dimensional Analysis, Quantum Probability and Related Topics 19, no. 03 (August 31, 2016): 1650016. http://dx.doi.org/10.1142/s0219025716500168.

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We study stochastic differential games of jump diffusions, where the players have access to inside information. Our approach is based on anticipative stochastic calculus, white noise, Hida–Malliavin calculus, forward integrals and the Donsker delta functional. We obtain a characterization of Nash equilibria of such games in terms of the corresponding Hamiltonians. This is used to study applications to insider games in finance, specifically optimal insider consumption and optimal insider portfolio under model uncertainty.
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41

Dragone, Davide, Luca Lambertini, George Leitmann, and Arsen Palestini. "Hamiltonian Potential Functions for Differential Games." IFAC Proceedings Volumes 42, no. 2 (2009): 1–8. http://dx.doi.org/10.3182/20090506-3-sf-4003.00002.

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42

Eidel'man, S. D., Alexey A. Chikriy, and Alexander G. Rurenko. "Linear Integro-Differential Games of Approach." Journal of Automation and Information Sciences 31, no. 1-3 (1999): 1–13. http://dx.doi.org/10.1615/jautomatinfscien.v31.i1-3.20.

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43

Chikriy, Alexey A., and O. M. Patlanzhoglu. "Some Conjugate Differential Games of Pursuit." Journal of Automation and Information Sciences 31, no. 4-5 (1999): 33–42. http://dx.doi.org/10.1615/jautomatinfscien.v31.i4-5.60.

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44

Brambilla, Chiara, and Luca Grosset. "Free final time Stackelberg differential games." International Mathematical Forum 17, no. 2 (2022): 67–74. http://dx.doi.org/10.12988/imf.2022.912312.

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45

Averboukh, Yu V. "Randomized Nash equilibrium for differential games." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 27, no. 3 (September 2017): 299–308. http://dx.doi.org/10.20537/vm170301.

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46

Prince, Eric R., Joshuah A. Hess, Richard G. Cobb, and Ryan W. Carr. "Elliptical Orbit Proximity Operations Differential Games." Journal of Guidance, Control, and Dynamics 42, no. 7 (July 2019): 1458–72. http://dx.doi.org/10.2514/1.g004031.

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47

Zhang, Feng. "Stochastic differential games involving impulse controls." ESAIM: Control, Optimisation and Calculus of Variations 17, no. 3 (April 23, 2010): 749–60. http://dx.doi.org/10.1051/cocv/2010023.

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48

Lehrer, Ehud, and Ady Pauzner. "Repeated Games with Differential Time Preferences." Econometrica 67, no. 2 (March 1999): 393–412. http://dx.doi.org/10.1111/1468-0262.00024.

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49

Chistyakov, Sergei, and Fedor Nikitin. "On value operators in differential games." Applied Mathematical Sciences 9 (2015): 2941–52. http://dx.doi.org/10.12988/ams.2015.52133.

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50

Smol’yakov, E. R. "Differential games on partially overlapping sets." Differential Equations 47, no. 12 (December 2011): 1817–27. http://dx.doi.org/10.1134/s001226611112010x.

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