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

Author

Listed:
  • DeBlassie, Dante
  • Smits, Robert G.

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.

Suggested Citation

  • DeBlassie, Dante & Smits, Robert G., 2013. "The tug-of-war without noise and the infinity Laplacian in a wedge," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4219-4255.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:12:p:4219-4255
    DOI: 10.1016/j.spa.2013.06.011
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