November 5 (Thursday) 10:00-11:00, room E.118.2 (main building, 1st floor)
János Flesch (Maastricht University, The Netherlands)
Decision problems with rare interventions
We consider infinite-horizon decision problems in which the decision maker loses control at randomly selected stages. We model this as a two-player game between the decision maker and an adversary. At each stage, exactly one player is active: the decision maker is active with probability 1-p, and the adversary is active with probability p. The active player chooses an action from a finite action set. The decision maker wins if the resulting infinite sequence of actions belongs to a given set W, which is assumed to be Borel with respect to the product topology.
We show that, for each set W, the decision maker’s winning probability converges to either 0 or 1 as p tends to 0. We call a set W robustly winning if this limit is 1, and a strategy of player 1 robustly epsilon-winning if it guarantees a winning probability of at least 1-epsilon for all sufficiently small p. We characterize the robustly winning sets and show that, for every robustly winning set and every positive epsilon, the decision maker has a robustly epsilon-winning strategy.
The talk is based on joint work with Galit Ashkenazi-Golan, Arkadi Predtetchinski,and Eilon Solan.