The tug-of-war without noise and the infinity Laplacian in a wedge

Dante DeBlassie and Robert G. Smits

Stochastic Processes and their Applications, 2013, vol. 123, issue 12, 4219-4255

Abstract: Consider the ending time of the tug-of-war without noise in a wedge. There is a critical angle for finiteness of its expectation when player I maximizes the distance to the boundary and player II minimizes the distance. There is also a critical angle such that for smaller angles, player II can find a strategy where the expected ending time is finite, regardless of player I’s strategy. For larger angles, for each strategy of player II, player I can find a strategy making the expected ending time infinite. Using connections with the inhomogeneous infinity Laplacian, we bound this critical angle.

Keywords: Tug-of-war without noise; Wedge; Inhomogeneous game ∞-Laplacian; Viscosity solution; Expected time to end the game; Critical angle (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spa.2013.06.011

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