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Stochastic nonzero-sum games: a new connection between singular control and optimal stopping

Tiziano de Angelis and Giorgio Ferrari
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Tiziano de Angelis: Center for Mathematical Economics, Bielefeld University
Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University

No 565, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: In this paper we establish a new connection between a class of 2-player nonzerosum games of optimal stopping and certain 2-player nonzero-sum games of singular control. We show that whenever a Nash equilibrium in the game of stopping is attained by hitting times at two separate boundaries, then such boundaries also trigger a Nash equilibrium in the game of singular control. Moreover a differential link between the players' value functions holds across the two games.

Keywords: games of singular control; games of optimal stopping; Nash equilibrium; onedimensional diffusion; Hamilton-Jacobi-Bellman equation; verification theorem (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth and nep-hpe
Date: 2016-07-21
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https://pub.uni-bielefeld.de/download/2904753/2904755 First Version, 2016 (application/x-download)

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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:565

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