Unique Ergodicity of Deterministic Zero-Sum Differential Games
Hochart
A
author
2021
English
We study the ergodicity of deterministic two-person zero-sum differential games. This property is defined by the uniform convergence to a constant of either the infinite-horizon discounted value as the discount factor tends to zero, or equivalently, the averaged finite-horizon value as the time goes to infinity. We provide necessary and sufficient conditions for the unique ergodicity of a game. This notion extends the classical one for dynamical systems, namely when ergodicity holds with any (suitable) perturbation of the running payoff function. Our main condition is symmetric between the two players and involve dominions, i.e., subsets of states that one player can make approximately invariant.
Differential games
Hamilton-Jacobi equations
Viscosity solutions
Ergodicity
Limit value
WOS:000527444200001
exported from refbase (show.php?record=1148), last updated on Thu, 11 Nov 2021 16:13:16 -0300
text
10.1007/s13235-020-00355-y
Hochart2021
Dynamic Games And Applications
Dyn. Games Appl.
2021
Springer Birkhauser
continuing
periodical
academic journal
11
109
136
2153-0785