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

In this note we prove an inequality involving primes and the product of consecutive primes.

We present a self-contained elementary and detailed exposition of Mertens' own proof of his theorem on the divergence of the series of the reciprocals of the primes and compare it with the modern proofs. His proof contains explicit…

Goedel's results have had a great impact in diverse fields such as philosophy, computer sciences and fundamentals of mathematics. The fact that the rule of mathematical induction is contradictory with the rest of clauses used by Goedel to…

We analyse a mathematical model of seeding for sports contests with round-robin qualifying tournaments. The standard seeding system based on coefficients measuring the historical performance of the teams is shown to be unfair as it might…

The proof of the Heisenberg uncertainty relation is modified to produce two improvements: (a) the resulting inequality is stronger because it includes the covariance between the two observables, and (b) the proof lifts certain restrictions…

We provide a systematic approach to deal with the following problem. Let $X_1,\ldots,X_n$ be, possibly dependent, $[0,1]$-valued random variables. What is a sharp upper bound on the probability that their sum is significantly larger than…

This paper provides an analysis of different formal representations of beliefs in epistemic game theory. The aim is to attempt a synthesis of different structures of beliefs in the presence of indeterminate probabilities. Special attention…

We have fundamentally corrected the proofs of the theorems from our paper [9] by giving an entirely different approach, using quite a simple method based on applications of some elementary inequalities, well-known H\"older's inequality, and…

Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.

A notion of incentive for agents is introduced which leads to a very general notion of an equilibrium for a finite game. Sufficient conditions for the existence of these equilibria are given. Known existence theorems are shown to be…

In the present paper, based on the previous work (Part I), we present a game semantics for the intensional variant of intuitionistic type theory that refutes the principle of uniqueness of identity proofs and validates the univalence axiom,…

We prove a new inequality for Gaussian processes, this inequality implies the Gordon-Chevet inequality. Some remarks on Gaussian proofs of Dvoretzky's theorem are given.

This paper shows that, for symmetric games in normal form, strategy profiles that satisfy Hofstadter's Superrationality criterion also satisfy both of Halpern's and Pass's criteria under Common Counterfactual Belief of Rationality:…

We construct games of chance from simpler games of chance. We show that it may happen that the simpler games of chance are fair or unfavourable to a player andyet the new combined game is favourable -- this is a counter-intuitive…

When testing a statistical hypothesis, is it legitimate to deliberate on the basis of initial data about whether and how to collect further data? Game-theoretic probability's fundamental principle for testing by betting says yes, provided…

B\'eal et al. (Int J Game Theory 54, 2025) introduce the Diversity Owen value for TU-games with diversity constraints, and provide axiomatic characterizations using the axioms of fairness and balanced contributions. However, there exist…

We define a version of the Ehrenfeucht-Fra\"iss\'e game in the setting of metric model theory and continuous first-order logic and show that the second player having a winning strategy in a game of length $n$ exactly corresponds to being…

We study an elementary inequality supporting the classical Hermite-Hadamard inequality in the matrix setting. This leads to a number of interesting matrix inequalities such new Schatten p-norm estimates and new majorization

The purpose of the paper is to present an short proof of the Chuang's inequality.

We investigate the Friedman--Goldfarb--Harrington theorem from two perspectives. Firstly, in the frameworks of classical and modal propositional logics, we study the forms of sentences whose existence is guaranteed by the FGH theorem.…