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math.PR2026
On the Trail of Lost Pennies: player-funded tug-of-war on the integers
Alan Hammond
We study random-turn resource-allocation games. In the Trail of Lost Pennies, a counter moves on . At each turn, Maxine stakes and Mina $b \in [0,\in…
math.PR2026
Stake-governed tug-of-war and the biased infinity Laplacian
Yujie Fu, Alan Hammond, Gábor Pete
In tug-of-war, two players compete by moving a counter along edges of a graph, each winning the right to move at a given turn according to the flip of a possibly biased coin. The g…