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Bad(s,t) is hyperplane absolute winning

Erez Nesharim, David Simmons (2014)

Acta Arithmetica

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.

Banach-Mazur game played in partially ordered sets

Wiesław Kubiś (2016)

Banach Center Publications

Concepts, definitions, notions, and some facts concerning the Banach-Mazur game are customized to a more general setting of partial orderings. It is applied in the theory of Fraïssé limits and beyond, obtaining simple proofs of universality of certain objects and classes.

Banzhafův index a dvoustupňové hlasovací systémy

Antonín Slavík (2017)

Pokroky matematiky, fyziky a astronomie

V textu představíme tzv. Banzhafův index, který umožňuje kvantifikovat sílu voliče v předepsaném hlasovacím systému. Definice indexu je zcela elementární, podrobnější zkoumání jeho vlastností však vede k zajímavé a hlubší matematice. Výklad je ilustrován řadou konkrétních příkladů ze světa politiky; uvidíme, že díky Banzhafovu indexu se matematika dostala i na stránky novin.

Bilateral sequential bargaining with perfect information and different protocols

Robert Golański (2006)

Banach Center Publications

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...

Bi-personal stochastic transient Markov games with stopping times and total reward criterion

Martínez-Cortés Victor Manuel (2021)

Kybernetika

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...

Boundary-influenced robust controls: two network examples

Martin V. Day (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the differential game associated with robust control of a system in a compact state domain, using Skorokhod dynamics on the boundary. A specific class of problems motivated by queueing network control is considered. A constructive approach to the Hamilton-Jacobi-Isaacs equation is developed which is based on an appropriate family of extremals, including boundary extremals for which the Skorokhod dynamics are active. A number of technical lemmas and a structured verification theorem...

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