Nonzero-Sum Stochastic Differential Games with Impulse Controls: A Verification Theorem with Applications

We consider a general nonzero-sum impulse game with two players. The main mathematical contribution of this paper is a verification theorem that provides, under some regularity conditions, a suitable system of quasi-variational inequalities for the payoffs and the strategies of the two players at so...

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Hlavní autori: Aïd, René, Basei, Matteo, Callegaro, Giorgia, Campi, Luciano, Vargiolu, Tiziano
Médium: Paper
Jazyk:English
Vydavateľské údaje: St. Louis Federal Reserve Bank of St. Louis 01.02.2020
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Equilibrium
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Abstract We consider a general nonzero-sum impulse game with two players. The main mathematical contribution of this paper is a verification theorem that provides, under some regularity conditions, a suitable system of quasi-variational inequalities for the payoffs and the strategies of the two players at some Nash equilibrium. As an application, we study an impulse game with a one-dimensional state variable, following a real-valued scaled Brownian motion, and two players with linear and symmetric running payoffs. We fully characterize a family of Nash equilibria and provide explicit expressions for the corresponding equilibrium strategies and payoffs. We also prove some asymptotic results with respect to the intervention costs. Finally, we consider two further nonsymmetric examples where a Nash equilibrium is found numerically.
AbstractList We consider a general nonzero-sum impulse game with two players. The main mathematical contribution of this paper is a verification theorem that provides, under some regularity conditions, a suitable system of quasi-variational inequalities for the payoffs and the strategies of the two players at some Nash equilibrium. As an application, we study an impulse game with a one-dimensional state variable, following a real-valued scaled Brownian motion, and two players with linear and symmetric running payoffs. We fully characterize a family of Nash equilibria and provide explicit expressions for the corresponding equilibrium strategies and payoffs. We also prove some asymptotic results with respect to the intervention costs. Finally, we consider two further nonsymmetric examples where a Nash equilibrium is found numerically.
Author Campi, Luciano
Vargiolu, Tiziano
Basei, Matteo
Callegaro, Giorgia
Aïd, René
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  surname: Aïd
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  givenname: Matteo
  surname: Basei
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  givenname: Giorgia
  surname: Callegaro
  fullname: Callegaro, Giorgia
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  givenname: Luciano
  surname: Campi
  fullname: Campi, Luciano
– sequence: 5
  givenname: Tiziano
  surname: Vargiolu
  fullname: Vargiolu, Tiziano
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