A Two-Player Zero-sum Game Where Only One Player Observes a Brownian Motion

Fabien Gensbittel and Catherine Rainer ()
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Catherine Rainer: Université de Bretagne Occidentale

Dynamic Games and Applications, 2018, vol. 8, issue 2, No 4, 280-314

Abstract: Abstract We study a two-player zero-sum game in continuous time, where the payoff—a running cost—depends on a Brownian motion. This Brownian motion is observed in real time by one of the players. The other one observes only the actions of his/her opponent. We prove that the game has a value and characterize it as the largest convex subsolution of a Hamilton–Jacobi equation on the space of probability measures.

Keywords: Zero-sum continuous-time game; Incomplete information; Hamilton–Jacobi equations; Brownian motion; Measure-valued process; 91A05; 91A23; 49N70 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s13235-017-0219-5

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