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

Jewaidu Rilwan (), Pasquale Fotia () and Massimiliano Ferrara ()
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Jewaidu Rilwan: Bayero University Kano
Pasquale Fotia: University Mediterranea of Reggio Calabria
Massimiliano Ferrara: University Mediterranea of Reggio Calabria

Decisions in Economics and Finance, 2023, vol. 46, issue 1, No 11, 319-333

Abstract: 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.

Keywords: Game value; Grönwall-type constraints; Pursuit-evasion differential game; Optimal strategy; Attainability domain; 91A23; 91A10; 49N70; 49N90; 34H05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10203-023-00389-y

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