Geodesic
Non-Constant Discounting in Differential Games with Random Duration
Contributions to game theory and management, Tome 3 (2010), pp. 267-279

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Previous results on non-constant discounting in continuous time are extended to the field of deterministic differential games with a stochastic terminal time. Different cooperative and non-cooperative solution concepts for differential games with random duration are analyzed. The results are illustrated by solving the cake-eating problem describing the classical model of management of a nonrenewable resource for a logarithmic utility function. Time-consistency in cooperative differential games with non-constant discounting is briefly discussed.
Keywords: non-constant discounting, naive and sophisticated agents, random duration, differential games, non-renewable resources. 
@article{CGTM_2010_3_a20,
     author = {Jes\'us Mar{\'\i}n-Solano and Ekaterina V. Shevkoplyas},
     title = {Non-Constant {Discounting} in {Differential} {Games} with {Random} {Duration}},
     journal = {Contributions to game theory and management},
     pages = {267--279},
     publisher = {mathdoc},
     volume = {3},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2010_3_a20/}
}
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Jesús Marín-Solano; Ekaterina V. Shevkoplyas. Non-Constant Discounting in Differential Games with Random Duration. Contributions to game theory and management, Tome 3 (2010), pp. 267-279. http://geodesic.mathdoc.fr/item/CGTM_2010_3_a20/