Generalized Differential Games

E. N. Barron () and K. T. Nguyen ()
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E. N. Barron: Loyola University Chicago
K. T. Nguyen: North Carolina State University

Dynamic Games and Applications, 2023, vol. 13, issue 3, No 1, 705-720

Abstract: Abstract An important generalization of a Nash equilibrium is the case when the players must choose strategies which depend on the other players. The case in zero-sum differential games with players y and z when there is a constraint of the form $$g(y,z) \le 0$$ g ( y , z ) ≤ 0 is introduced. The Isaacs’ equations for the upper value and the lower value of a zero-sum differential game are derived and a condition guaranteeing existence of value is derived. It is also proved that the value functions are the limits of penalized games.

Keywords: Differential games; Isaacs’ equation; Generalized game; Hamilton–Jacobi; Viscosity solution; Control constraints; 49L25; 49L20; 91A23 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13235-022-00452-0

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