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 Gronwall-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 Gronwall-type optimal strategies for the players. The constructed strategies are then employed in establishing that the estimated game value is guaranteed for the players.
On game value of a differential game problem with Grönwall-type constraints on players control functions / Rilwan, J.; Fotia, P.; Ferrara, M.. - In: DECISIONS IN ECONOMICS AND FINANCE. - ISSN 1593-8883. - 46:1(2023), pp. 319-333. [10.1007/s10203-023-00389-y]
On game value of a differential game problem with Grönwall-type constraints on players control functions
Fotia P.Membro del Collaboration Group
;Ferrara M.
Supervision
2023-01-01
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 Gronwall-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 Gronwall-type optimal strategies for the players. The constructed strategies are then employed in establishing that the estimated game value is guaranteed for the players.File | Dimensione | Formato | |
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