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On game value of a differential game problem with Grönwall-type constraints on players control functions

Author

Listed:
  • Jewaidu Rilwan

    (Bayero University Kano)

  • Pasquale Fotia

    (University Mediterranea of Reggio Calabria)

  • Massimiliano Ferrara

    (University Mediterranea of Reggio Calabria
    Bocconi University)

Abstract

The game value of a pursuit-evasion differential game is an estimation of the game’s payoff at the instant when all the players employ their optimal strategies. In this paper, we estimate this value for a fixed duration differential game problem of countably many pursuers and one evader with the Grönwall-type constraints, a generalization of the well known geometric constraints, imposed on all the players’ control functions. The players’ dynamics are governed by a generalized dynamic equations. We construct the attainability domain and a Grönwall-type optimal strategies for the players. The constructed strategies are then employed in establishing that the estimated game value is guaranteed for the players.

Suggested Citation

  • Jewaidu Rilwan & Pasquale Fotia & Massimiliano Ferrara, 2023. "On game value of a differential game problem with Grönwall-type constraints on players control functions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 319-333, June.
    • Handle: RePEc:spr:decfin:v:46:y:2023:i:1:d:10.1007_s10203-023-00389-y
    DOI: 10.1007/s10203-023-00389-y
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    References listed on IDEAS

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    1. Gafurjan I. Ibragimov & Mehdi Salimi, 2009. "Pursuit-Evasion Differential Game with Many Inertial Players," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-15, September.
    2. Idris Ahmed & Poom Kumam & Gafurjan Ibragimov & Jewaidu Rilwan & Wiyada Kumam, 2019. "An Optimal Pursuit Differential Game Problem with One Evader and Many Pursuers," Mathematics, MDPI, vol. 7(9), pages 1-11, September.
    3. Mehdi Salimi & Massimiliano Ferrara, 2019. "Differential game of optimal pursuit of one evader by many pursuers," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 481-490, June.
    Full references (including those not matched with items on IDEAS)

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