相关论文: Hoeffding's inequality in game-theoretic probabili…

An argument is provided for the equality case of the high dimensional Bonnesen inequality for sections. The known equality case of the Bonnesen inequality for projections is presented as a consequence.

We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.

De Finetti's betting argument is used to justify finitely additive probabilities when only finitely many bets are considered. Under what circumstances can countably many bets be used to justify countable additivity? In this framework, one…

We show that the higher-order matching problem is decidable using a game-theoretic argument.

Probabilistic concurrent/distributed strategies have so far not been investigated thoroughly in the context of imperfect information, where the Player has only partial knowledge of the moves made by the Opponent. In a situation where the…

We present an analog of O'Neill's Theorem (Theorem 5.2 in [17]) for finite games, which reveals some of the structure of equilibria under payoff perturbations in finite games.

Ehrenfeucht-Fra\"iss\'e games provide a fundamental method for proving elementary equivalence (and equivalence up to a certain quantifier rank) of relational structures. We investigate the soundness and completeness of this method in the…

Consider concurrent, infinite duration, two-player win/lose games played on graphs. If the winning condition satisfies some simple requirement, the existence of Player 1 winning (finite-memory) strategies is equivalent to the existence of…

The expected utility hypothesis is a popular concept in economics that is useful for making decisions when the payoff is uncertain. In this paper, we investigate the implications of a fluctuation theorem in the theory of expected utility.…

An inequality in quantum mechanics, which does not appear to be well known, is derived by elementary means and shown to be quite useful. The inequality applies to 'all' operators and 'all' pairs of quantum states, including mixed states. It…

We present a new variant of the potential game and show that certain compact subsets of $\R^n$, including a large class of self-affine sets, are winning in our game. We prove that sets with sufficiently strong winning conditions are…

In this note we prove the uniqueness of solutions to a class of Mean Field Games systems subject to possibly degenerate individual noise. Our results hold true for arbitrary long time horizons and for general non-separable Hamiltonians that…

The purpose of this paper is to provide a random version of Simons' inequality.

The main purpose of the present article is to give some new Hilbert's sum type inequalities, which in special cases yield the classical Hilbert's inequalities. Our results provide some new estimates to these types of inequalities.

We propose a new interpretation of the strange phenomena that some authors have observed about the Wald game. This interpretation is possible thanks to the new language of \emph{loadings} that Morrison and the author have introduced in a…

In this short note, we provide an inequality that holds in any finite group, only involving the orders of the elements; we prove that equality holds if and only if the group is nilpotent.

The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

Truth, consistency and elementary equivalence can all be characterised in terms of games, namely the so-called evaluation game, the model-existence game, and the Ehrenfeucht-Fraisse game. We point out the great affinity of these games to…

In this note we study how to share a good between n players in a simple and equitable way. We give a short proof for the existence of such fair divisions.