Strongly Time-Consistent Core in Differential Games with Discrete Distribution of Random Time Horizon

• Autorzy: Malakhova A. P. , Gromova E. V.

Identyfikatory

DOI

10.14708/ma.v46i2.5135

Warianty tytułu

PL

Silnie zgodny w czasie rdzeń gry różniczkowej z dyskretnym losowym horyzontem

• Języki publikacji: EN

Abstrakty

EN

In this paper we investigate the problem of strong time-consistency of the core for a particular class of differential games with random time horizon, namely, it is assumed that there exists a set of probabilities of the end of the game at discrete time instants. A condition guaranteeing the strong time consistency of the core is presented.

PL

Przedmiotem badań jest problem silnej zgodności w czasie rdzenia dla konkretnej klasy gier różniczkowych z losowym horyzontem czasowym. Zakłada się, że rozkład czasu trwania gry jest rozkładem dyskretnym z pewnej ustalonej rodziny. Podano warunek, przy którym mamy silną spójność czasową rdzenia.

Słowa kluczowe

EN

differential games; random time horizon; cooperative solution; strong time-consistency; core; discrete distribution; imputation distribution procedure

PL

ATR; Wip1; model matematyczny; UV; p53

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2018
• Tom: Vol. 46, no. 2
• Strony: 197--209
• Opis fizyczny: Bibliogr. 30 poz., fot., rys.

Twórcy

autor

Malakhova A. P.

• Saint-Petersburg State University, Graduate School of Management 3, Volkhovskiy per., St. Petersburg, 199004, Russia

autor

Gromova E. V.

• Saint-Petersburg State University, Graduate School of Management 3, Volkhovskiy per., St. Petersburg, 199004, Russia

Bibliografia

• [1] Başar, Tamer and Olsder, Geert Jan. Dynamic noncooperative game theory. Academic Press, Ltd., London, second edition, 1995. ISBN 0-12-080221-X. Cited on p. 197.
• [2] Bulgakova, M. and Petrosyan, L. . Strongly time-consistent core in multistage games. In L. N. Polyakova, editor, 2017 Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V.F. Demyanov) (CNSA), pages 55-58, Saint-Petersburg, Russia, 2017. ISBN 978-1-5090-6260-7. doi: 10.1109/CNSA.2017.7973942. Cited on p. 198.
• [3] Dockner, Engelbert and Jorgensen, Steffen and Long, Ngo and Sorger, Gerhard. Differential Games in Economics and Management Science. Cambridge University Press, 2000. URL https://EconPapers.repec.org/RePEc:cup:cbooks:9780521637329. Cited on p.197.
• [4] Germain, Marc and Tulkens, Henry and Magnus, Alphonse. Dynamic core-theoretic cooperation in a two-dimensional international environmental model. Mathematical Social Sciences, 59 (2): 208-226, March 2010. URL https://ideas.repec.org/a/eee/matsoc/v59y2010i2p208-226.html. Cited on p. 198.
• [5] Gromov D. and Gromova E. Differential Games with Random Duration: A Hybrid Systems Formulation. Contributions to Game Theory and Management, 7:104-119, 2014. ISSN 2310-2608. Cited on p. 198.
• [6] Gromov D. and Gromova E. On a class of hybrid differential games. Dynamic Games and Applications, 7 (2): 266-288, 2017. ISSN 2153-0785. doi: 10.1007/s13235-016-0185-3. Cited on p. 198.
• [7] Gromova E. The Shapley value as a sustainable cooperative solution in differential games of 3 players. In ecent Advances in Game Theory and Applications, Static and Dynamic Game Theory: Foundations and Applications, pages 67-90. Springer International, Heidelberg, 2016. doi: 10.1007/978-3-319-43838-2-4. Cited on p. 198.
• [8] Gromova E. and Malakhova A. and Palestini A. Payoff distribution in a multi-company extraction game with uncertain duration. submitted to Special Issue ’’Mathematical Game Theory” in Mathematics, 2017. Cited on p. 197.
• [9] Gromova E. and Tur A. Differential game of pollution control with random terminal instants. In Abstracts of the tenth International Conference on Game Theory and Management, page 53, 2016. Cited on p. 198.
• [10] Gromova E. and Tur A. On the form of integral payoff in differential games with random duration. In 2017 XXVI International Conference on Information, Communication and Automation Technologies (ICAT), pages 1-6, Oct 2017. doi: 10.1109/ICAT.2017.8171597. Cited on p. 197.
• [11] John von Neumann and Oskar Morgenstern and Harold W. Kuhn and Ariel Rubinstein. Theory of Games and Economic Behavior (60th Anniversary Commemorative Edition). Princeton University Press, 1944. ISBN 9780691130613. URL http://www.jstor.org/stable/j.ctt1r2gkx. Cited on p. 198.
• [12] Kranich, Laurence and Perea, Andres and Peters, Hans. Core concepts for dynamic tu games. International Game Theory Review, 07 (01): 43-61, 2005. doi: 10.1142/S0219198905000417. URL https://doi.org/10.1142/S0219198905000417. Cited on p. 198.
• [13] Kuzyutin D. and Gromova E. and Pankratova Ya. Sustainable cooperation in multicriteria multistage games. working paper, 2017. Cited on p. 198.
• [14] Malakhova, A. On the dynamic stability of optimality principles in a differential game with random duration (in Russian). In N. V. Smirnov, editor, The XLVIII annual international conference on Control Processes and Stability (CPS 17), page 117. St. Petersburg: Publishing House, 2017. Маланова А. П. О динамической устойчивости принципов оптимальности в одной дифференциальной игре со случайным моментом окончаниа//Процессы управления и устойчивость. 2017. T. 4 (20). No. 1. C. 652-656. Cited on pp. 198 and 201.
• [15] Marín-Solano, Jesús and Shevkoplyas, Ekaterina V. Non-constant discounting and differential games with random time horizon. Automatica, 47 (12): 2626-2638, Dec. 2011. ISSN 0005-1098. doi: 10.1016/j.automatica.2011.09.010. URL http://dx.doi.org/10.1016/j.automatica.2011.09.010. Cited on p. 197.
• [16] Parilina E. and Petrosyan L. Strongly subgame consistent core in stochastic games (in Russian). Mat. Teor. Igr Prilozh., 9 (2): 39-61, 2017. ISSN 2074-9872. Елена М. Парилина, Леон A. Петросян: Сильно позиционно состоятельное с-ядро в стохастических играх. МТИП 9 (2): 39-61, 2017. MathNet.ru:mgta198. Zbl 06822825. Cited on p. 198.
• [17] Petrosyan L. The stability of solutions in n-person differential games. Vestn. Leningr. Univ., Mat. Mekh. Astron., 1977 (4): 46-52, 1977. ISSN 0024-0850. Петросян Л. A. Устойчивость решений дифференциальных игр со многими участниками, Вестник Ленинградского университета. Сериа 1: математика, механика, астрономия, no. 19, pp. 46-52, 1977. Zbl 0397.90116. Cited on p. 198.
• [18] Petrosyan L. On new strongly time-consistent optimality principles in cooperative differential games. Proc. Steklov Institute of mathematics. Ser. Optimal control and differential equations, 211: 370-376, 1995. Петросян Л. A. (1995). O новых cильно динамических устойчивых принципах оптимальности в кооперативных дифференциальных играх. Труды математического института им. Стеклова „Оптимальное управление и дифференциальные управнения” (pp. 370-376). Издательство „Наука”. Cited on p. 198.
• [19] Petrosyan L. and Danilov N. Cooperative differential games and their applications. Irkutsk State University, 1985. Петросян Л. A., Данилов H.H. Kooпepaтивные дифференциальные игры и их приложения. Иркутский государственный университет, 1985. 276 p. Cited on pp. 197 and 198.
• [20] Petrosyan L. and Murzov N. Game-theoretic problems of mechanics. Litovsk. Mat. Sb., 6: 423-433, 1966. ISSN 0132-2818. MR 0211764. Cited on p. 197.
• [21] Petrosyan L. and Pankratova Ya. Construction of strongly time-consistent subcores in differential games with prescribed duration. Trudy Inst. Mat. i Mekh. UrO RAN, 23 (1): 219-227, 2017. ISSN 0134-4889. doi: 10.21538/0134-4889-2017-23-1-219-227. Панкратова, Я. Б., Петросян Л. A., Построение cильно-динамически устойчивых подъядер в дифференциальных играх с предписанной продолжительностью. Труды института математики и механики YPO PAH, 23 (1), 219-227, 2017. Cited on p. 198.
• [22] Petrosyan L. and Shevkoplyas E. Cooperative differential games with stochastic time. Vestnik St Petersburg University Mathematics, 33 (4): 18-23, 2000. Петросян Л. A., Шевкопляс E. B. Kooпepaтивные дифференциальные игры со случайной продолжительностью. Вестник Санкт-Петербургского университета. Сериа 1: математика, механика, астрономия. No. 4. pp. 14-18, 2000. Cited on p. 197.
• [23] Petrosyan O. and Gromova E. and Pogozhev S. Strong time-consistent subset of core in cooperative differential games with finite time horizon. Mat. Teor. Igr Pril., 8 (4): 79-106, 2016. ISSN 2074-9872. Ованес Л. Петросян, Екатерина В. Громова, Cepгей B. IIoложев, “O cильно динамически устойчивом подмножестве C-ядрa в kooпepaтивных дифференциальных игрaх с предписанной продолжительностью” МТИП, 8: 4 (2016), 79-106. Cited on p. 198.
• [24] Громова, E. B. and Петросян Л. A., Cильно динамически устойчивое kooпepaтивное решение в одной дифференциальной игре управления вредными выбросами. УБС, Специальный выпуск 55: 140-159, 2015. Gromova, E. B. and Petrosyan, L. A. Sil’no dinamiceski ustoichivoe kooperativnoe reshenie v odnoi differencial’noi igre upravlenja vrednvmi vybrosami UBS - 2015. – Special’nyi vypusk No 55. - S. 140-159. (in Russian). MathSciRu, eLibrary.ru:id=23769383. Cited on p. 198.
• [25] Громова, E. B. and Петросян Л. A., Cильно динамически устойчивое kooпepaтивное решение в одной дифференциальной игре управления вредными выбросами. УБС, Специальный выпуск 55: 140-159, 2015. Gromova, E. B. and Petrosyan, L. A. Sil’no dinamiceski ustoichivoe kooperativnoe reshenie v odnoi differencial’noi igre upravlenja vrednvmi vybrosami UBS - 2015. – Special’nyi vypusk No 55. - S. 140-159. (in Russian). MathSciRu, eLibrary.ru:id=23769383. Cited on p. 198.
• [26] Sedakov A. The strong time-consistent core. Mat. Teor. Igr Pril., 7 (2): 69-84, 2015. ISSN 2074-9872. Aptеm A. Cедаков, “O cильной динамической устойчивости c-ядрa”, MTИII, 7: 2 (2015), 69-84; Autom. Remote Control, 79: 4 (2018), 757-767. Cited on p. 198.
• [27] Shapley, Lloyd S. Cores of convex games. International Journal of Game Theory, 1 (1): 11-26, Dec 1971. ISSN 1432-1270. doi: 10.1007/BF01753431. URL https://doi.org/10.1007/BF01753431. Cited on p. 198.
• [28] Shevkoplyas E. Stable cooperation in differential games with random duration. Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2 (3): 79-105, 2010. ISSN 2074-9872. Екатерина B. Шевкопляс, “Yстойчивая kooпepaция в kooпepaтивных дифференциальных игрaх со случайной продолжительностью”, MTИII, 2: 3 (2010), 79-105. Cited on p. 198.
• [29] Yaari and Menahem E. Uncertain Lifetime, Life Insurance, and the Theory of the Consumer. Review of Economic Studies, 32 (2): 137-150, 1965. URL https://EconPapers.repec.org/RePEc:oup:restud:v:32: y: 1965:i:2:p:137-150. Cited on p. 197.
• [30] Yeung D. W. K. and Petrosyan L. A. Cooperative Stochastic Differential Games. Springer Verlag, 2006. ISBN 0-387-27620-3. Cited on pp. 197 and 198.

Uwagi

Pkt. 25 – to powtórzenie punktu 24.

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).