J. An proved that for any s,t ≥ 0 such that s + t = 1, Bad (s,t) is (34√2)¯¹-winning for Schmidt's game. We show that using the main lemma from [An] one can derive a stronger result, namely that Bad (s,t) is hyperplane absolute winning in the sense of [BFKRW]. As a consequence, one can deduce the full Hausdorff dimension of Bad (s,t) intersected with certain fractals.

Most research done in the bargaining literature concentrates on the situations in which players get to be proposers alternately, with the first player being the proposer in the first period, the second player being the proposer in the second period, and so on until the cycle ends and the order of proposers is repeated. However, allowing for only this kind of order is a rather simplifying assumption. This paper looks at the situation in which we allow for much more general kind of protocols. We characterize...

The article is devoted to a class of Bi-personal (players 1 and 2), zero-sum Markov games evolving in discrete-time on Transient Markov reward chains. At each decision time the second player can stop the system by paying terminal reward to the first player. If the system is not stopped the first player selects a decision and two things will happen: The Markov chain reaches next state according to the known transition law, and the second player must pay a reward to the first player. The first player...