Closed-loop Nash equilibrium for a partial differential game with application to competitive personalized advertising

Speaker(s)

Dominika Machowska

Affiliation

Uniwersytet Łódzki

Date

March 9, 2022, 12:15 p.m.

Information about the event

4060 oraz https://us02web.zoom.us/j/89788218933?pwd=aVc2UHdwRWMwZy8yK24rQTJWRW42QT09 Meeting ID: 897 8821 8933 Passcode: Biomat

Seminar

Seminar of Biomathematics and Game Theory Group

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This paper is devoted to an N-person partial differential game whose dynamics of the state variable is described by a hyperbolic differential equation with certain boundary and initial conditions while the objective of each player is given by a finite horizon accumulated payoff functional with discounting. We extend the concept of a closed-loop Nash equilibrium for a partial differential game with the dynamics of the states described by a hyperbolic differential equation (a transport equation). We propose the definition of a dual closed-loop Nash equilibrium for which we give sufficient conditions. Moreover, we present the relationship between the Nash equilibria with the dual closed-loop and the classical closed-loop information structure.We apply the new results to the goodwill dynamics model in which the goodwill is influenced by personalized advertising and customers’ recommendations for which we construct a dual closed-loop Nash equilibrium and we examine its economic properties.

This is a joint work with Andrzej Nowakowski (UŁ) and Agnieszka Wiszniewska-Matyszkiel (UW).

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