Nonzero-Sum Stochastic Impulse Games with an Application in Competitive Retail Energy Markets

被引:0
|
作者
Aid, Rene [1 ]
Ben Ajmia, Lamia [2 ]
Gaigi, M'hamed [2 ]
Mnif, Mohamed [2 ]
机构
[1] PSL Res Univ, Univ Paris Dauphine, LEDa, Paris, France
[2] Univ Tunis El Manar, ENIT Lamsin, Tunis, Tunisia
关键词
Stochastic impulse games; Nash equilibrium; viscosity solution; FUNCTIONAL QUANTIZATION; DIFFERENTIAL-GAMES; LIQUIDITY RISK;
D O I
10.1051/cocv/2023089
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
We study a nonzero-sum stochastic differential game with both players adopting impulse controls, on a finite time horizon. The objective of each player is to maximize her total expected discounted profits. The resolution methodology relies on the connection between Nash equilibrium and the corresponding system of quasi-variational inequalities (QVIs in short). We prove, by means of the weak dynamic programming principle for the stochastic differential game, that the equilibrium expected payoff of each player is a constrained viscosity solution to the associated QVIs system in the class of linear growth functions. We also introduce a family of equilibrium expected payoffs converging to our equilibrium expected payoff of each player, and which is characterized as the unique constrained viscosity solutions of an approximation of our QVIs system. This convergence result is useful for numerical purpose. We apply a probabilistic numerical scheme which approximates the solution of the QVIs system to the case of the competition between two electricity retailers. We show how our model reproduces the qualitative behavior of electricity retail competition.
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页数:42
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