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Open Access ·Peer-reviewed·ISSN (Online): 2169-0103·ISSN (Print): 0252-2667

WoS  JIF 2026 : 0.4 (Q4)

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Open Access Research Article

Differential games with fractional payoffs

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pp. 1489–1513Vol. 47Issue 4April 2026DOI: 10.47974/JIOS-1961XML
Received:
02 Oct 2023
Published Online:
26 Mar 2026
Article type:
Research Article
Language:
EN
Article no.:
JIOS-1961
Pages:
1489–1513

Abstract

This paper provides a formulation for new differential games with fractional payoffs. By applying the standard argument used in mathematical programming theory, we show that the saddle point function and the equilibrium point exist in these games. 

Keywords

Subject Classifications

49N7091A23

References

[1] Walid Abdelfattah, A parametric approach to solve neutrosophic linear programming models, Journal of Information and Optimization Sciences, vol. 42, no. 3, pp. 631-654 (2021).
[2] Vijay Kumar Aggarwal, Ramaswamy Chandrasekaran, and Kunhiraman P.K. Nair, Markov ratio decision processes, Journal of Optimization Theory and Applications, vol. 21, pp. 27-37 (1977).
[3] Vijay Kumar Aggarwal, Ramaswamy Chandrasekaran, and Kunhiraman P.K. Nair, Discounted stochastic ratio games, SIAM Journal on Discrete Mathematics, vol. 1, no. 2, pp. 201-210 (1980).
[4] Alain Bensoussan and Avner Friedman, Nonlinear Variational Inequalities and Differential Games with Stopping Times, Journal of Functional Analysis, vol. 16, pp. 305-352 (1974).
[5] Alain Bensoussan and Jacques-Louis Lions, Applications of variational inequalities in stochastic control , North Holland (1982).
[6] Suresh K. Bhatt, An existence theorem for a fractional control problem, Journal of Optimization Theory and Applications, vol. 11, pp. 379-385 (1973).
[7] Werner Dinkelbach, On nonliner fractional programming, Management Science, vol. 13, no. 7, pp. 492-498 (1967).
[8] Bennett Fox, Markov renewal programming by linear fractional programming, SIAM Journal on Applied Mathematics, vol. 14, no. 6, pp. 1418-1432 (1966).
[9] Avner Friedman, Differential games, Dover Publications (2006).
[10] Seiichi Iwamoto and Toshiharu Fujita, Markov decision processes under fractional criterions (In Japanese), Kyoto University, RIMS, Kokyuroku, vol. 1079, pp. 153-163 (1999).
[11] Hang-Chin Lai, On a dynamic fractional game, Journal of Mathematical Analysis and Applications, vol. 294, pp. 644-654 (2004).
[12] Hiroaki Morimoto, On average cost stopping time problems, Probability Theory Related Fields, vol. 90, pp. 469-490 (1991).
[13] Makiko Nisio, Stochastic differential games and viscosity solutions of Isaacs equations, Nagoya Mathematical Journal, vol.110, pp.163-184 (1988).
[14] Zhiyuan Ren and Bruce Krogh, Markov decision processes with fractional costs, IEEE Transaction on Automatic Control, vol. 50, pp. 646-650 (2005).
[15] Yoichi Sawasaki, Yutaka Kimura, and Kensuke Tanaka, A two-person zero-sum game with fractional loss function, Journal of the Operations Research Society of Japan, vol. 43, pp. 209-218 (2000).
[16] Roger G. Schroeder, Linear programming solutions to ratio games, Operations Research, vol. 18, pp. 300-305 (1970).
[17] Ioan Mihai Stancu-Minasian, Fractional programming, Kluwer Academic Publishers (1997).
[18] John von Neumann, A model of general economic equilibrium, Review of economic studies, vol. 13, no. 1, pp. 1-9 (1945).

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