The game of Double-Silver on intervals (Q5954648)

In Silverman's game, there is a single threshold and penalty for both players; in double-silver, there is a threshold and penalty for each player. Suppose that the strategy set for player 1 is \((1,B)\); for player 2 \((A,D)\). This paper computes a value for double-silver in the following three cases: the threshold for player \(B\) is less than \(A\); \(1< A\) and player 2's penalty does not occur; \(A=1\). The paper conjectures that these are the only cases for which a value exists.