Luciano Campi (LSE) et Giorgia Callegaro (Università di Padova)

Abstract: We study the notion of Nash equilibrium in a general nonzero-sum impulse game for two players. The main mathematical contribution of the paper is a verification theorem which provides, under some regularity conditions, the system of quasi-variational inequalities identifying the value functions and the optimal strategies of the two players. As an application, we propose a model for the competition among retailers in electricity markets. We first consider a simplified one-player setting, where we obtain a quasi-explicit expression for the value function and the optimal control. Then, we turn to the two-player case and we provide a detailed heuristic analysis of the retail impulse game, conducted along the lines of the verification theorem obtained in the general setting. This allows to identify reasonable candidates for the intervention and continuation regions of both players and their strategies.

This talk is based on a joint work with R. Aid, M. Basei, G. Callegaro and T. Vargiolu.