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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - Jesús Marín-Solano
AU  - Ekaterina V. Shevkoplyas
TI  - Non-Constant Discounting in Differential Games with Random Duration
JO  - Contributions to game theory and management
PY  - 2010
SP  - 267
EP  - 279
VL  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2010_3_a20/
LA  - en
ID  - CGTM_2010_3_a20
ER  - 
%0 Journal Article
%A Jesús Marín-Solano
%A Ekaterina V. Shevkoplyas
%T Non-Constant Discounting in Differential Games with Random Duration
%J Contributions to game theory and management
%D 2010
%P 267-279
%V 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2010_3_a20/
%G en
%F CGTM_2010_3_a20
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/

[1] Ainslie G. W., Picoeconomics, Cambridge University Press, Cambridge, UK, 1992

[2] Alj A., Haurie A., “Dynamic Equilibria in Multigeneration Stochastic Games”, IEEE Transactions on Automatic Control, 28 (1983), 193–203 | DOI | MR | Zbl

[3] Barro R. J., “Ramsey meets Laibson in the neoclassical growth model”, Quarterly Journal of Economics, 114 (1999), 1125–1152 | DOI | Zbl

[4] Boukas E. K., Haurie A., Michel P., “An Optimal Control Problem with a Random Stopping Time”, Journal of Optimization Theory and Applications, 64:3 (1990), 471–480 | DOI | MR | Zbl

[5] Burness H. S., “A Note on Consistent Naive Intertemporal Decision Making and an Application to the Case of Uncertain Lifetime”, Review of Economic Studies, 43:3 (1976), 547–549 | DOI | Zbl

[6] Ekeland I., Lazrak A., Equilibrium policies when preferences are time inconsistent, 2008, arXiv: 0808.3790v1 [math.OC]

[7] Friedman A., Differential games, Conference board of the Mathematical Sciences, Regional Conference Series in Mathematics, 18, American Mathematical Society, 1974 | MR | Zbl

[8] Karp L., “Non-constant discounting in continuous time”, Journal of Economic Theory, 132 (2007), 557–568 | DOI | MR | Zbl

[9] Loewenstein G., Prelec D., “Anomalies in intertemporal choice: evidence and an interpretation”, Quarterly Journal of Economics, 57 (1992), 573–598 | DOI

[10] Marín-Solano J., Navas J., “Non-constant discounting in finite horizon: The free terminal time case”, Journal of Economic Dynamics and Control, 33:3 (2009), 666–675 | DOI | MR | Zbl

[11] Petrosjan L. A., Murzov N. V., “Game-theoretic problems of mechanics”, Litovsk. Mat. Sb., 6 (1966), 423–433 (in Russian) | MR | Zbl

[12] Petrosjan L. A., Shevkoplyas E. V., “Cooperative differential games with stochastic time”, Vestnik St. Petersburg Univ. Math., 33:4 (2000), 14–18 (in Russian) | MR

[13] Petrosjan L. A., Zaccour G., “Time-consistent Shapley Value Allocation of Pollution Cost Reduction”, Journal of Economic Dynamics and Control, 27 (2003), 381–398 | DOI | MR | Zbl

[14] Petrosjan L. A., Zenkevich N. A., Game Theory, Series on Optimization, 3, World Scientific, 1996 | MR

[15] Phelps E. S., Pollak R. A., “On Second-best National Saving and Game-Equilibrium Growth”, Review of Economic Studies, 35 (1968), 185–199 | DOI

[16] Pollak R. A., “Consistent Planning”, Review of Economic Studies, 35 (1968), 201–208 | DOI

[17] Shevkoplyas E. V., “On the construction of the characteristic function in differential games with random duration”, Control Theory and Theory of Generalized Solutions of Hamilton–Jacobi Equations, Proceedings of International Seminar CGS'2005 (Ekaterinburg, Ural Univ., Russia, 2006), v. 1, 285–293 (in Russian)

[18] Strotz R. H., “Myopia and Inconsistency in Dinamic Utility Maximization”, Review of Economic Studies, 23 (1956), 165–180 | DOI

[19] Thaler R., “Some empirical evidence on dynamic inconsistency”, Economics Letters, 8 (1981), 201–207 | DOI

[20] Yaari M. E., “Uncertain Lifetime, Life Insurance, and the Theory of the Consumer”, The Review of Economic Studies, 32:2 (1965), 137–150 | DOI