Nonzero-Sum Games of Optimal Stopping for Markov Processes

Nonzero-Sum Games of Optimal Stopping for Markov Processes

Optimal Stopping Games for Markov Processes

where the horizon T (the upper bound for τ and σ above) may be either finite or infinite (it is assumed that G1(XT ) = G2(XT ) if T is finite and lim inft→∞G2(Xt) ≤ lim supt→∞G1(Xt) if T is infinite). If X is right-continuous, then the Stackelberg equilibrium holds, in the sense that V ∗(x) = V∗(x) for all x with V := V ∗ = V∗ defining a measurable function. If X is right-continuous and left-co...

Nash Equilibrium in Nonzero-Sum Games of Optimal Stopping for Brownian Motion

Stochastic nonzero-sum games: a new connection between singular control and optimal stopping

In this paper we establish a new connection between a class of 2-player nonzerosum games of optimal stopping and certain 2-player nonzero-sum games of singular control. We show that whenever a Nash equilibrium in the game of stopping is attained by hitting times at two separate boundaries, then such boundaries also trigger a Nash equilibrium in the game of singular control. Moreover a different...

Optimal Stopping Problems for Some Markov Processes

In this paper, we solve explicitly the optimal stopping problem with random discounting and an additive functional as cost of observations for a regular linear diffusion. We also extend the results to the class of one-sided regular Feller processes. This generalizes the result of Beibel and Lerche [Statist. Sinica 7 (1997) 93–108] and [Teor. Veroyatn. Primen. 45 (2000) 657–669] and Irles and Pa...