On a regular tree, assign each vertex a random independent
value. Two players alternate choosing a child of the current vertex.
When reaching level n, player 1 pays player 2 the cumulative sum of the
values along the chosen path.
We show that in certain cases the value of this game converges as
n\to\infty, and discuss the challenges in extending our results.
Joint with Gourab Ray and Yinon Spinka.