Related papers: A game for Baire's grand theorem
This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…
We prove game-theoretic generalizations of some well known zero-one laws. Our proofs make the martingales behind the laws explicit, and our results illustrate how martingale arguments can have implications going beyond measure-theoretic…
A classic model to study strategic decision making in multi-agent systems is the normal-form game. This model can be generalised to allow for an infinite number of pure strategies leading to continuous games. Multi-objective normal-form…
We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose…
Schmidt games and the Cantor winning property give alternative notions of largeness, similar to the more standard notions of measure and category. Being intuitive, flexible, and applicable to recent research made them an active object of…
Schmidt's game is a powerful tool for studying properties of certain sets which arise in Diophantine approximation theory, number theory, and dynamics. Recently, many new results have been proven using this game. In this paper we address…
We generalize a concept of classical finite extensive game to make it useful for application of quantum objects. The generalization extends a quantum realization scheme of static games to any finite extensive game. It represents an…
We present a version of so called formula size games for regular expressions. These games characterize the equivalence of languages up to expressions of a given size. We use the regular expression size game to give a simple proof of a known…
Consider a game where Alice generates an integer and Bob wins if he can factor that integer. Traditional game theory tells us that Bob will always win this game even though in practice Alice will win given our usual assumptions about the…
Bayesian regression games are a special class of two-player general-sum Bayesian games in which the learner is partially informed about the adversary's objective through a Bayesian prior. This formulation captures the uncertainty in regard…
We give an elementary proof that in a Borel family of games, the set of games for which player II has a winning strategy is Baire measurable, universally measurable, and completely Ramsey in the case where $X = [\mathbb{N}]^{\aleph_0}$.
Genericity is the idea that the same program can work at many different data types. Longo, Milstead and Soloviev proposed to capture the inability of generic programs to probe the structure of their instances by the following equational…
We prove two determinacy and decidability results about two-players stochastic reachability games with partial observation on both sides and finitely many states, signals and actions.
We present a version of the Banach-Mazur game, where open sets are replaced by elements of a fixed partially ordered set. We show how to apply it in the theory of Fraisse limits and beyond, obtaining simple proofs of universality of certain…
In Solovay model it is shown that the duality principle between the measure and the Baire category holds true with respect to the sentence - "The domain of an arbitrary generalized integral for a vector-function is of first category."
We establish a connection between two well-studied spaces of countable groups: the space of group operations and the space of marked groups. This connection shows that the two spaces are equivalent in terms of generic properties in the…
We study a generalisation of B\"uchi-Landweber games to the timed setting. The winning condition is specified by a non-deterministic timed automaton with epsilon transitions and only Player I can elapse time. We show that for fixed number…
This paper has two central aims: first, to provide simple conditions under which the generalized games in choice form and, consequently, the abstract economies, admit equilibrium; second, to study the solvability of several types of systems…
The Baire category theorem states that every complete pseudometric space is a Baire space. There are some results in metric spaces which have their analogue in uniform spaces, however this is not one of them. Nonetheless, since the Baire…
We show that the modular term condition higher commutator is equal to the modular hypercommutator. As a consequence, we arrive at a new proof that HC8 holds for modular varieties. Next, we develop a procedure for a modular variety for…