William D. Sudderth

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Consider a process X(·) = {X(t), 0 ≤ t <∞} with values in the interval I = (0, 1), absorption at the boundary-points of I, and dynamics dX(t) = β(t)dt+ σ(t)dW (t), X(0) = x. The values (β(t), σ(t)) are selected by a controller from a subset of <× (0,∞) that depends on the current position X(t), for every t ≥ 0. At any stopping rule τ of his choice, a second(More)
Flesch et al [3] showed that, if the payoff functions are bounded and lower semicontinuous, then such a game always has a pure, subgame perfect -equilibrium for > 0. Here we prove the same result for bounded, upper semicontinuous payoffs. Moreover, Example 3 in Solan and Vieille [7] shows that if one player has a lower semicontinuous payoff and another(More)