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Nash equilibrium structure of Cox process Hotelling games

Part of: Stochastic processes Game theory

Published online by Cambridge University Press:  06 June 2022

Venkat Anantharam  and
François Baccelli Open the ORCID record for François Baccelli [Opens in a new window]
Venkat Anantharam*
Affiliation:
University of California, Berkeley
François Baccelli*
Affiliation:
INRIA-ENS, Paris
*
*Postal address: University of California, Berkeley, USA. Email address: [email protected]
**Postal address: INRIA-ENS, Paris, France. Email address: [email protected]
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Abstract

We study an N-player game where a pure action of each player is to select a nonnegative function on a Polish space supporting a finite diffuse measure, subject to a finite constraint on the integral of the function. This function is used to define the intensity of a Poisson point process on the Polish space. The processes are independent over the players, and the value to a player is the measure of the union of her open Voronoi cells in the superposition point process. Under randomized strategies, the process of points of a player is thus a Cox process, and the nature of competition between the players is akin to that in Hotelling competition games. We characterize when such a game admits Nash equilibria and prove that when a Nash equilibrium exists, it is unique and consists of pure strategies that are proportional in the same proportions as the total intensities. We give examples of such games where Nash equilibria do not exist. A better understanding of the criterion for the existence of Nash equilibria remains an intriguing open problem.

Keywords

Constant-sum gameCox processgame theoryHotelling competitionNash equilibriumPoisson process

MSC classification

Primary: 60G55: Point processes
Secondary: 91A06: $n$-person games, $n>2$ 91A60: Probabilistic games; gambling
Type
Original Article
Information
Advances in Applied Probability , Volume 54 , Issue 2 , June 2022 , pp. 570 - 598
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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