Geodesic
A policy iteration algorithm for nonzero-sum stochastic impulse games
René Aïd1 ; Francisco Bernal2 ; Mohamed Mnif3 ; Diego Zabaljauregui4 ; Jorge P. Zubelli5
1 Université Paris Dauphine, PSL Research University, LEDA
2 CMAP, Ecole Polytechnique, and Finance for Energy Market Research Centre (FiME)
3 University of Tunis El Manar, ENIT-LAMSIN
4 Department of Statistics, London School of Economics and Political Science
5 IMPA
ESAIM. Proceedings, Tome 65 (2019), pp. 27-45.

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This work presents a novel policy iteration algorithm to tackle nonzero-sum stochastic impulse games arising naturally in many applications. Despite the obvious impact of solving such problems, there are no suitable numerical methods available, to the best of our knowledge. Our method relies on the recently introduced characterisation of the value functions and Nash equilibrium via a system of quasi-variational inequalities. While our algorithm is heuristic and we do not provide a convergence analysis, numerical tests show that it performs convincingly in a wide range of situations, including the only analytically solvable example available in the literature at the time of writing.
DOI : 10.1051/proc/201965027

René Aïd 1 ; Francisco Bernal 2 ; Mohamed Mnif 3 ; Diego Zabaljauregui 4 ; Jorge P. Zubelli 5

1 Université Paris Dauphine, PSL Research University, LEDA
2 CMAP, Ecole Polytechnique, and Finance for Energy Market Research Centre (FiME)
3 University of Tunis El Manar, ENIT-LAMSIN
4 Department of Statistics, London School of Economics and Political Science
5 IMPA 
@article{EP_2019_65_a2,
     author = {Ren\'e A{\"\i}d and Francisco Bernal and Mohamed Mnif and Diego Zabaljauregui and Jorge P. Zubelli},
     title = {A policy iteration algorithm for nonzero-sum stochastic impulse games},
     journal = {ESAIM. Proceedings},
     pages = {27--45},
     publisher = {mathdoc},
     volume = {65},
     year = {2019},
     doi = {10.1051/proc/201965027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201965027/}
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René Aïd; Francisco Bernal; Mohamed Mnif; Diego Zabaljauregui; Jorge P. Zubelli. A policy iteration algorithm for nonzero-sum stochastic impulse games. ESAIM. Proceedings, Tome 65 (2019), pp. 27-45. doi : 10.1051/proc/201965027. http://geodesic.mathdoc.fr/articles/10.1051/proc/201965027/

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