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.
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This work was partially supported by a grant from the Simons Foundation
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Jewaidu Rilwan and Massimiliano Ferrara. The first draft of the manuscript was written by Pasquale Fotia. All authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Rilwan, J., Fotia, P. & Ferrara, M. On game value of a differential game problem with Grönwall-type constraints on players control functions. Decisions Econ Finan 46, 319–333 (2023). https://doi.org/10.1007/s10203-023-00389-y
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DOI: https://doi.org/10.1007/s10203-023-00389-y
Keywords
- Game value
- Grönwall-type constraints
- Pursuit-evasion differential game
- Optimal strategy
- Attainability domain