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Journal articles on the topic 'Differential games'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Platzer, André. "Differential Hybrid Games." ACM Transactions on Computational Logic 18, no. 3 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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

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11

Browne, Sid. "Stochastic differential portfolio games." Journal of Applied Probability 37, no. 01 (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

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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 (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 (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 (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 act

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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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (2012): 317–32. http://dx.doi.org/10.1007/s11401-012-0716-1.

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37

Agranov, Marina, Jeongbin Kim, and Leeat Yariv. "Coordination with Differential Time Preferences: Experimental Evidence." American Economic Review: Insights 6, no. 4 (2024): 543–57. http://dx.doi.org/10.1257/aeri.20230234.

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The experimental literature on repeated games has largely focused on settings where players discount the future identically. In applications, however, interactions often occur between players whose time preferences differ. We study experimentally the effects of discounting differentials in infinitely repeated coordination games. In our data, differential discount factors play two roles. First, they provide a coordination anchor: more impatient players get higher payoffs first. Introducing even small discounting differentials reduces coordination failures significantly. Second, with pronounced

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38

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 b

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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 str

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40

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 (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

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41

Kim, Arkady V. "Introduction to the theory of positional differentional games of systems with aftereffect (based on the i-smooth analisys methodology)." Russian Universities Reports. Mathematics, no. 147 (2024): 268–95. http://dx.doi.org/10.20310/2686-9667-2024-29-147-268-295.

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Although the foundations of the theory of positional differential games of systems with aftereffect described by functional differential equations (FDE) were developed back in the 1970s by N.N. Krasovsky, Yu.S. Osipov and A.V. Kryazhimsky, there are still no works that, similar to [N.N. Krasovsky, A.I. Subbotin. Positional Differential Games. Moscow: Nauka, 1974, 457 p.] (hereinafter referred to as [KS]), would represent a “complete” theory of positional differential games with aftereffect. The paper presents an approach to constructively transferring all the results of the book [KS] to system

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42

Draouil, Olfa, and Bernt Øksendal. "Stochastic differential games with inside information." Infinite Dimensional Analysis, Quantum Probability and Related Topics 19, no. 03 (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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43

FALCONE, M. "NUMERICAL METHODS FOR DIFFERENTIAL GAMES BASED ON PARTIAL DIFFERENTIAL EQUATIONS." International Game Theory Review 08, no. 02 (2006): 231–72. http://dx.doi.org/10.1142/s0219198906000886.

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In this paper we present some numerical methods for the solution of two-persons zero-sum deterministic differential games. The methods are based on the dynamic programming approach. We first solve the Isaacs equation associated to the game to get an approximate value function and then we use it to reconstruct approximate optimal feedback controls and optimal trajectories. The approximation schemes also have an interesting control interpretation since the time-discrete scheme stems from a dynamic programming principle for the associated discrete time dynamical system. The general framework for

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44

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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45

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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46

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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47

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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48

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

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49

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 (2019): 1458–72. http://dx.doi.org/10.2514/1.g004031.

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50

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

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